That's an America problem, not a capitalism problem. Free, or at least highly subsidised, higher education isn't exactly limited to communist countries.
Capitalism can keep people from studying because they need to work instead, or maybe they were in a low-income area and didn't get the chance to go to a good school to get the grades or knowledge they needed before higher education, etc.
Capitalism effects every facet of our lives, even in developed countries where we try to spend money to counter it's damages.
Doesn't really help if you never make it to uni because your parents weren't able and/or willing to help you out with schoolwork and couldn't afford/didn't care to get someone else to help you.
Bildungsferne is, sadly, often passed along from parents to children.
Even just free higher education is not enough under capitalism. You need to live somewhere and eat something while you learn. Also reminds me about one comment I wrote. Here's copy-pasta:
American "left": maybe we shold do some student debth relif? Just a tini-tiny. If you don't mind.
Rest of the world right: universal education, more funding!
Rest of the world center: universal education, state must provide students with everything(including housing and food) so they don't worry about anything else other than learning, state must provide teachers with everything(including decent salary) so they don't wory about anything else other than teaching, state must provide universities with all necessary equipment, buildings must be maintained in good condition(so ceiling wouldn't fall on students' and teachers' heads)!