Countries like the USA have a system with slightly less pretense. If you're part of the Olympic program you basically get paid a small living wage (but, importantly, all your expenses are paid for: food, medical care equipment, etc) to train full time.
The benefit of the soldier/police/... system is that you get education for another job on the side, so if your career breaks down for whatever reason you got a simpler transition into a "normal" job.
