First, the (widely known) problem that I thought about which inspired the idea: basically, how can you maintain academic standards for the class you are teaching, when so few of the students are really prepared to be successful.
Sure, you can just keep the standards high/static, fight cheating the best you can, and fail most of the students until you get fired. You could try to teach all the preliminary material yourself, trying to make up for years of poor education, but that's probably too much for the time you have and wastes the time of students already prepared.
But how about, instead, having a placement exam on Day 1? A qualifier, if you will. It would test a representative set of knowledge you should already have in order to be successful. The students who don't pass are dropped without judgement, and that's it. Nobody's time is wasted. You can move quickly through a wait-list if there is one, and few students will find themselves with a failing grade halfway through the course.
Thoughts?