Most of what I learned in college was only because I did homework and struggled to figure it out myself. Classroom time was essentially just a heads up to what I'll actually be learning myself later.

Granted, this was much less the case in grade school - but if students are going to see homework for the first time in college, I can see problems coming up.

If you got rid of homework throughout all of the "standard" education path (grade school + undergrad), I would bet a lot of money that I'd be much dumber for it.