As markets closed yesterday, Twitter’s stock sank to its lowest level ever — a drop that raised speculation, yet again, that another company would take it over. At only a $19 billion market valuation, that’s not a surprise.

Neither is the other company most often cited as its obvious buyer: Google.

“At some point, it is just simple math that Google grabs it,” said one person close to the situation. “Why they haven’t yet is a mystery.”

Indeed, at first glance, several reasons crop up for why Google would in fact be eager to buy the embattled social media service:

Google still doesn’t have social. It’s not for lack of trying, but the search giant’s myriad attempts to get big in social and best Facebook have largely been failures, starting way back when with Orkut (still big in Brazil!). After trying to goose its Google+ service by linking it with popular services, the company began last week to unbundle those other products, including YouTube, essentially hoisting the white flag on its attempt to build a logged-in social network.

Google lacks strong footing in two big areas where ad budgets are moving — mobile and native content. Twitter, despite its struggles to grow its user base, is the closest competitor to Facebook for those dollars.

Google likes information problems and loves to acquire companies and people working on them.

And, of course, Google has about $70 billion in cash lying around, more than enough to pay a premium for Twitter, whose price is so low that it is seen as a bargain.

It’s been an open secret in Silicon Valley that Google has kicked the tires on Twitter before — as has Facebook. But the last truly meaningful conversation between the two companies was around two years ago, before Twitter went public, according to sources familiar with the companies.

Still, that talk has gone nowhere, and there is good reason for that. Despite the seemingly natural fit, there is a just as strong if not stronger case that Google should not make the move.

Here are three key reasons, gleaned from talking to sources inside and outside the company.

Google already has everything it needs from Twitter: Earlier this year, the search giant inked two deals with the smaller company. The first brought tweets into search results, another step in Google’s push to remake search with more immediacy and relevancy. The second brought Twitter ads into Google’s massive ad server, DoubleClick, giving its customers another reason to stick around and not depart for Facebook.

Both deals help Twitter with its goal to spread tweets to logged-out eyeballs. It’s not a big leap to imagine tweets appearing under similar arrangements in other Google services, such as mapping. Most of Google’s products, save Google+ perhaps, reach far more than Twitter’s 304 million users a month. Google could begin integrating content from these logged-in tweeters without taking on a multi-billion dollar acquisition expense or the burden of solving Twitter’s ailing user growth problems.

Antitrust: The last thing Google needs is more government attention, which a high-profile acquisition of Twitter would surely attract. Regulators would be hard pressed not to press hard on a deal like this, especially after rivals chime in. The threat of government bodies spiking such a deal is likely a key inhibitor. While Google faced (and won) a challenge to its purchase of DoubleClick in 2007, that was for just $3.1 billion and was in a different era. A Twitter deal is likely to be seven times that amount, if not more.

Furthermore, the search giant is already enmeshed in a prickly European Union antitrust case, which could cost it up to a tenth of its annual sales if it loses. Ad tech companies are lobbying the EU to open another case, while rivals at home, like Yelp, are making the case to the Department of Justice and state attorneys general that Google’s behavior on search and mobile warrants action.

Should it move to buy Twitter, Google will have to be confident that it can make the case that the products and markets of the two companies are disparate enough.

It’s not a Larry-size problem: While the pace of Google’s acquisitions has slowed tremendously of late, the company has been adamant it is not relenting. If Twitter joins its ranks, it might operate as its own autonomous kingdom, much the same as several recent big purchases like Nest. Or it could fit in the nascent communications division, run by ads vet Nick Fox, or the remnants of Google+ under Bradley Horowitz (he now oversees photos, streams and sharing). Google has made it clear what the first product is, but not the latter two.

Yet the larger outstanding question is not where Twitter would sit. It’s why Larry Page would even want it at all.

Twitter does not crack the type of mammoth, earth-shattering problems Page thinks Google should take on, according to multiple people familiar with the CEO’s thinking. Look at the recent substantial acquisitions and investments Page has driven: Nest, for connected homes; Skybox, for satellite imaging; DeepMind, for the next evolution of artificial intelligence; Calico, for human longevity. And more: A cornucopia of robotics startups and a new company, Sidewalk Labs, to solve the problems of cities. Each of these has ambitious, almost patently absurd, goals, just the type Page seems to like.

Twitter, despite the lip service its mercurial CEOs have paid to its world-changing impact, just doesn’t fit the mold.

Additional reporting by Kara Swisher