I agree the way things are set up now the for-profit sector cashes in big time. (Quite a succesful lobby, I suppose). But would the costs not rise if attending college became free? Wouldn't everyone want to get in?
The issue is slightly different, the real task is to discourage those who won't finish their degree because they aren't cut out for it early on, so that the student and the university won't waste their time. When I got my degree back when in Europe they did just that. The attrition rate in the first year was high - 30 %, but whoever had passed the sieving exams usually came out at the other end with a degree.
Unfortunately one of the metrics US unis are judged by is retention rate. This will have to change.
I'm having trouble thinking of a downside to this.
It depends. Prices could go up as a result of cronyism and corruption. Or prices could go down if the deciders decide to cut it.
Or if education were democratically managed, resources could be allocated according to the population's preferences.
Who knows what would happen in real life?