Well, my first point would be that having "entertainers" representing colleges is really no different than having "entertainers" represent cities. Are all members of the Philadelphia Phillies part of the city of Philadelphia? One could argue that Colleges are different in that players should be students, but that is simply not reality. Some are, some are not. But somehow there needs to be a way to apprentice as a football player, and colleges are the current choice.
Well, I don't know that I would take it to "Strippers", but yes, they are only affiliated to the school. That is the current state for all of the major football universities. Currently, many of the players are exactly what you say in the 3rd paragraph, they are entertainers and many are not bona fide students. Some are, but why have people on campus that would not qualify as students and make no effort to get a degree? Why not let them chose if they want to pursue a higher education without the farce of fake classes? This is not limited to College Football, College Basketball is even worse really (how many years did Georgetown go without a player graduating? I forget, it was an amazing number at one point).
The truth is that their is no such thing as minor league football. If there was, then that would be fine, let them play there, but that is an infrastructure that does not exist. What does exist is an infrastructure built around colleges. This is different than baseball. I don't see a reasonable path to create this infrastructure and then you would have a split of players between the colleges and minor leagues that would create 2 leagues with lesser players than what exists now. This would never be acceptable to what are now College Football fans.
If there was minor league football than a large, large entertainment option would be eliminated (or radically changed). Living in the northeast that is less of an issue, but trust me College Football is THE SPORT of a large portion of the US, all of the Southeast and the Midwest. To completely gut this sport is not really realistic.
There is much talk about college football being a drain on finances. I don't believe this for a second. Not even close. It generates most of the income of the athletic department in all of the areas that College Football is king. I know it is foolish, but I know of MANY, MANY people that chose a college solely based on wanting to root for the team. That is genuinely foolish, but is common in the Southeast, in fact I would say it is the number one criteria used to select a college.