Although such jobs as teaching, police, doctors etc are important and fairly difficult, they do not need the same level of skill at what they do as a top class footballer needs to be successful.
People with special talents which entertain people on a large scale regularly will obviously earn a lot of money, and rightly so in my opinion.
Please don't tell me you just said Doctors don't require more skill than Footballers.
Tell my Dad that after 5 years of medical school and having spent 40 years working with his holiday's being taken up from retraining because medical procedures are ALWAYS changing. My Dad used to treat around 40 patients a day, which is around average, despite the fact he works in a small, specialist department, 90% of the time, those 40 patients would all have a different condition, which my Dad would have to identify, then treat continuously with the ultimate aim being a cure. So off hand my Dad would have to use 40 different procedures and be able to identify 40 different diaseases a day, and that's probably way under 2% of his overall knowledge. Then if you thrown on the fact he had to in 4 pages of paperwork to get those patients treated, and have to go teach some student teachers on various rare conditions as part of their course.
I could go on and on, and you made a point about Footballers having be to skilled, but you shot yourself in the foot the moment you said they had more required skill than a doctor.