Washington (CNN) Elizabeth Warren's new plan to cancel most student debt and make tuition free at public colleges is reopening a fight about the fairest way to make college more affordable.

The Massachusetts senator and Democratic presidential candidate this week proposed using her tax on America's richest families to radically reshape US higher education, and forgive outstanding student loans -- which top credit card and auto loan debt. Her plan would exclude the wealthiest borrowers from getting any debt relief.

But -- just as when independent Vermont Sen. Bernie Sanders proposed making tuition free during his 2016 Democratic presidential bid, or when New York Democratic Gov. Andrew Cuomo made tuition free in his state in 2017 -- Warren's plan is raising questions about who would benefit the most from the plan and whether taxpayer dollars will be well spent.

It's hard to please everyone with a debt forgiveness plan when some people choose less expensive colleges, taking on less or no debt, or have already made other sacrifices to pay off their loans.

But Warren's plan would offer debt relief based on income. Households that make less than $100,000 a year would get $50,000 in loan cancellation, with the amount of relief getting gradually smaller as income level goes up, and households that make more than $250,000 not eligible for any debt relief.

Warren also wants her plan to tackle the wealth gap, which has been exacerbated by student loan debt. She attempts to find a sweet spot between helping those struggling the most while excluding the richest Americans. A previous study suggested that a plan to wipe out all student debt, rather than limiting relief based on income, would increase the wealth gap.

study released this week by researchers at the Urban Institute found that the amount of debt forgiven under Warren's plan increases as household income increases, the report said, but drops for those in the top income quintile.

Yet some policy experts don't believe that looking at the total amount of dollars flowing to low-income students is the right metric for evaluating whether the policy is equitable or progressive.

"Regardless of dollar amount, the existence of debt is far riskier for low-income and middle-income households," said Mark Huelsman, associate policy director at the liberal think tank Demos.

"I think there is an interesting debate on the left now about whether progressive is just a matter of exactly where dollars flow vs. what the impact of the policy is -- how inclusive it is of everybody. I don't think there's a right answer, it comes down to value judgments," Huelsman added.

Borrowers with lower debt balances are more likely to default on their loans. Those with less than $5,000 in student debt account for about 35% of defaults, according to government data

Many of those struggling the most to pay down their debt would likely see it wiped away under Warren's plan. According to analysis provided by her campaign, 86% of people in the bottom two income quintiles would receive full student loan cancellation.

"This is a highly progressive proposal -- we're taxing the fortunes of people with over $50 million in wealth to provide student loan debt cancellation to 42 million lower-income and middle-class Americans," said a Warren campaign aide in a statement provided to CNN.

The issue is that people from higher-income households are more likely to go to college, and more likely to take out bigger student loans, said Matthew Chingos, director of the Center on Education Data and Policy at the Urban Institute and one of the authors of the study.

Chingos and his coauthor Kristin Blagg also found that Warren's plan would achieve one of its goals to help narrow the racial wealth gap. Their report said that 25% of all canceled debt dollars would go to black households, while they make up only 16% of all households receiving debt forgiveness.

But a more targeted approach to canceling student debt may be cheaper. Warren's campaign estimates it would cost $640 billion to offer the debt relief.

The government already offers loan forgiveness plans for certain students. Struggling borrowers can enroll in an income-driven plan that typically cancels remaining undergraduate debt after paying it down for 20 years, or 25 years for graduate debt. Other programs offer relief to those in public sector jobs and for those who went to for-proft schools that closed while they were enrolled.

Borrowers have complained that these plans are complicated and the Department of Education has recently come under fire for delaying relief for defrauded students

If students from wealthier households are more likely to go to college, then the tuition-free part of Warren's plan could be seen as sending too many taxpayer dollars to those who don't need help. It doesn't exclude students from rich families from benefiting -- though it calls for spending an extra $100 billion over 10 years on grants for low-income students to help them pay for housing, food, books, and child care.

Some form of free college has risen in popularity since Sanders helped make the idea mainstream. Several states and cities have adopted tuition-free policies since then and 2020 candidates including Sens. Cory Booker of New Jersey, Kamala Harris of California, and Kirsten Gillibrand of New York have all endorsed a debt-free college proposal.

Not everyone in the Democratic field embraces the idea. Pete Buttigieg, the mayor of South Bend, Indiana, said last month that "as a progressive, I have a hard time getting my head around the idea." He argued that making college free would be asking lower-income Americans to help subsidize those headed for higher-paying careers.

But Progressive Change Campaign Committee has thrown its support behind Warren's plan.

"We urge all Democratic candidates to match Elizabeth Warren's bold ideas on student debt so that our side can inspire new voters and be even better positioned to defeat Trump in 2020," said co-founder Adam Green.