TL;DR:

Amending the constitution is a very difficult task, rarely done, and only then with overwhelming support.

Repealing the second amendment alone doesn't ban guns. It just makes the matter less clear at best.

Adding an amendment that allows congress to make the stricter laws about guns is fraught with problems that have nothing to do with guns and you'll find with any contraband item.

Passing gun laws is a good political dream. Enforcing strict gun laws is a logistical nightmare (also a dream).

Those in opposition are to Gun Reform in the United States are very likely to not give up quietly on the matter.

As a general rule of any political reform, it is easier to build a political opposition to a proposed law than it is to build political support. Those trying to make the change have to make arguments that the change is for the better without proof. It's easier to resist.

Because of the constitution, which has a few broad legal interpretations that tie Government's hands and not just on gun control. As a general principle, the only legal entity that can violate the constitution is the government. It's also generally understood that the following three things are true about what the government can and cannot do:

If the Constitution says the government can do it, than the government can do it (called the no duh rule).

If the Constitution says the Government cannot do it, than the government cannot do it (also a No duh rule. Blocking the government from doing things is what most of the Bill of Rights is all about.).

If the Constitution does not say anything that allows the government can do a thing nor does it say the government cannot do a thing, than the government still cannot do a thing (again, spelled out in the 9th amendment which says in prettier words that no one should ever assume that the people do not have a right to do a thing just because the Constitution doesn't list the right, and the 10th Amendment which blocks the government from doing anything which hasn't been explicitly discussed in the constitution.).

With that in mind, we can now discuss the reforms and in fact, we have precedence for how we can get the government to ban things that is historical.

First, we know that the 2nd Amendment is interpreted as allowing people to own arms (guns are thought up first, but I can also own swords, knives, clubs, nun-chucks, lightsabers, yo-yos (those were originally developed as weapons), etc) and requires the government to show why a specific arm may not be considered necessarily part of a well regulated militia. So while guns are more likely to be used in a militia, nothing is stopping me from charging enemies on a modern battlefield with a yo-yo. If I stop a threat with a yo-yo, more power to me, but that's not likely to happen (hence why yo-yo bans aren't requested... people don't use them in self defense much anymore because they are not effective. If you are legally found to have kill a man in self-defense with a yo-yo, you are not held legally liable for his death same as if you did it with a gun. And go you, that's a badass claim to make the next time someone threatens you. I'm not messing with a man who killed a dude with a yo-yo, even if it wasn't self defense.)

So, anyway, the logical cry to allow for better reform is to repeal the second amendment. So let's go that route. First, amending the Constitution is hard and in 200+ years it's been successfully amended 27 times. This is an average of about an amendment once per decade, which dwindles when you consider the first ten were done pretty much all at once, one amendment repealed another one that was a bad idea, and the most recent amendment took two hundred years from start to finish to get through the process.

There are two ways to do this: Both Houses of Congress pass the bill by 2/3rds majority, and 3/4ths of the states pass the amendment in their legislatures (by their own rules of what percentage of quorum is required... only one state has a legislature with one house, so basically you need 38 states to vote on the bill twice, with two different pool of voters and there are only 99 total pools of voters and in all cases, you have to do it with the right combo of two out of those 99 pools. Basically a whole lot of people have to agree. That's the SIMPLE way to do this.

The second way is to call a constitutional convention and vote on the amendment. No one wants to do this. To the point that of the 27 amendments made, all of them were made by the first method. Part of the problem is the rules are clear on how to start one, but not clear if you can limit the proposals or if new introduce other proposals too. The threat to the parts of the Constitution people like (like the third amendment. No one has ever had a problem with that... really, it's never been the part of a major legal battle in 200 years. Don't put soldiers in peoples houses is something we all like) that nobody wants to risk throwing out the baby with the bathwater.

For argument's sake, let's say we've successfully repealed the Constitution. Hooray we've taken away the right to own guns!

Except we haven't. We've just eliminated the fact that it is explicitly stated that the government cannot do it. We still have the ninth amendment amendment that says "Just because it isn't written here doesn't mean it is not a right of the people." and the tenth amendment that says "If it isn't list here the government cannot do it." All we've done is allowed the states to ban guns (it's hard to enact gun control measures nationally, but states have an easier time because the 10th amendment says the right devolves to either the state level laws or to the people). Basically it means the courts would have to address the matter of if it's a state or people's right (and currently it's the right of the people by SCOTUS rule) but it could be found that states may ban guns if they so wish, but it won't be uniform across the nation. California might ban guns, but Texas won't.

Now, wait. Didn't the constitution once ban booze? That was a thing!

Actually, no, the constitution never banned booze, it allowed for the banning of booze. "The Prohibition Amendment" or 18th Amendment does not have any possible reading that bans booze. All it does is grant the federal government the power to regulate the sale of alcoholic beverages. Congress enacted a certain law that banned the sale, but under the 18th Amendment, they could also write a law that made beer legal but not whiskey or some other option. In fact, the law couldn't totally ban selling alcohol. It still had to comply with the first amendment and certain religions did use the consumption alcohol in religious ceremonies and production and sale for those reasons was exempt. Additionally, none of the ingredients to make alcohol was banned as they are common to other products. And while telling people how to break the law with your product in excruciating detail is not protected free speech, warning people to not break the law by doing certain things is perfectly legal. Thus resulting in the sale of grapes with a warning label that read like a cookbook for wine (Warning: Storing this product with sugar and yeast for extended periods of time in an oxygen deprived environment can result in a chemical reaction that creates illicit alcoholic beverage. We are not responsible for any adverse actions taken against the user for improper storage of this product.), and a few even list the exact ratio of ingredients that would cause the breech of the law. You know, for... safety reasons...

Suffice to say, the law was broken often, repeatedly, and with intent and the government was woefully unequipped to enforce the new law. People didn't stop drinking, they drank more. And you couldn't stop people from buying things to make alcohol, because most had non-alcoholic products that could be made from them, or even eaten outright themselves. Additionally, since it was now a federal power exclusively, the states couldn't enforce the ban. Most federal level crimes have a state level crime and while both the state and feds can enforce the crime anywhere in the U.S., the States usually enforce it. The feds only jump in if it's not a state crime, or crosses state or national borders, or if the state doesn't enforce their law. Consider Jessie Smollet, who is not being charged by Illinois, but is still under investigation for postal fraud, which is a federal crime that Illinois couldn't enforce even if it wanted to.

So we added another amendment to remove the 18th amendment, which meant that now the sale and production of alcohol was no longer in the constitution, which means that alcohol was again not commented on in the constitution and thus wasn't something the federal government could make laws about, so all Federal laws were null and void. States and local governments still could, but most didn't because they wanted to tax the sale and a ban on sales defeats that goal (a few localities are dry by law, but it's not nearly universal. The factory that produces Jack Daniels is famously located in a county that is dry by law (for sale purposes, not production purposes, allowing Jack to still make and sell whiskey, just not to stores in its home county or in the gift shop at the end of the factory tour. Samples are free, which means no sale involved... so...).

So, why are we talking about alcohol when the question is about guns? Well, as two great things that should NEVER go together, the principal still holds: Prohibition doesn't work when the majority of the population doesn't agree. While it was cited that 75 million house holds have at least one gun, that's households and the amount of gun owners varies wildly. Many gun owners do own multiple guns and surveys suggest that the majority of gun holders own more than one. And it's difficult to specify a typical average number because a lot of admitted owners and admitted multiple owners refuse to answer to a specific number other (other than more than one. Some don't even respond if they are even owners.). Many see firearms as a a security measure for their home and one of the first rule of any security feature is to not discuss specifics of that feature with people who don't need to know. To say nothing of the people being surveyed who own guns illegally.

A better statistic is that in the United States, for a population of 100,000 people, there are 105,000 guns (both legal and illegal). Or more simply put, there are more publicly available guns than there are people to fire them. Now, the problem with Prohibition is it wasn't agreed about by most Americans and the government got so fed up with trying to enforce it, that it finally gave up and said we don't want to do this. And to this day, you don't hear a lot about the feds arresting pot smokers in Colorado even though they do have jurisdiction to enforce drug laws there, do you?

So take all that, and then add that many gun owners meet the threat of ban or tougher restrictions with a defiant "You and what army" attitude. And before you answer with "um... the United States army, duh" keep in mind the constitution has some pretty hard rules about using the army against the citizens of the U.S. So it falls on law enforcement, which is a bit more on par with your average citizens. And the typically don't get involved when the states can do it. There are some states that do not want to enforce immigration laws for the feds... taking a bullet for the feds is a much taller order than detaining someone who overstayed his visa.