You're also overlooking the rising value, and rising recognized value, of a college degree. Since 1979, only college-educated workers have seen median wages rise. A high school diploma earned a -27% real return over the same period. Is it any surprise young people are encouraged and willing to pay anything, anything for a shot at economic opportunity? (Further information at epi.org.)
The rise in public university tuition is largely explained by reduced subsidies. Year after year, states "hold the line" on higher education spending, leaving ever more of the cost to students (and students' families, of course). To the point that California famously once spent more on college than prisons, and now spends more on prisons than college.
Grants and loans have been around for a long time. I'm not saying they're the cause of rising tuition. I'm saying increasing them wouldn't help.
I agree that the value of a college degree has a lot to do with increased tuition costs. If the average person will earn more than a $1 million more over his lifetime for getting a college degree, even expensive college is still "a good deal".
Take a look ITT. They took billions per year of poorly spent government grants, and left taxpayers on the hook for hundreds of millions. That school would not have existed were it not for federal grants.
Separating the payer from the decision maker yields very uneconomical decisions, in education, healthcare, whatever.
There are two options (1) restore sanity by regulating the hell out of education pricing or (2) restore sanity with market pressure.
I lean towards #2, but either way, grants aren't effective at lowering costs.