I haven't seen a study on this, but it's always the example I think should be studied when talking about MMT and "just print money" to pay for stuff.
To me, this is an example of printing money that's bad. We're throwing in huge amounts of extra government money directly competing with private money for the same demand. Which has the obvious side effect of that competition, huge inflation and increased costs.
All of which makes this a bad way to "allow everyone to get a college education". More state school funding and directly providing people an education would work better than giving everyone money to compete with in private institutions. Might have a different side effect, it could drive a huge demand for more staff, creating salary pressure which raises costs, and then causes tuition to increase anyway. There's more layers involved in that math with more indirection which probably dampens the impact some.
It would still be a good study to read and how it compares to other things we spend money on like a firehose. In case anyone has some "light" reading to share.