It's not that the schools enroll more than they can teach. One simple reason is that many classes are just very popular, word gets around that they are great for whichever reason (professor, easy A, really fun project, etc). If a class can only hold 20 people, and its a popular class, its going to fill up as soon as registration opens.
In the end, you aren't left without being able to take classes. Just possibly not the ones you wanted
In the UK you start a degree as a group and do all the same classes all at the same time as your peers. If you have a choice of classes then each of those choices can accommodate the whole group at the same time if everyone chose it, so classes just can’t be too full. At least this was the case at both use UK universities I’ve been to.
In the end, you aren't left without being able to take classes. Just possibly not the ones you wanted
I doubt this isn't the case in the UK too