Yes all expensive players train fast, the value of a player tells you how fast he develops. And after they are 22 they don't train fast anymore. They cant get 1* by their own at this point.
But I still keep my players beyond 22 most of the times. If they are unbalanced you can easily train them every season a bit with some rests so that they reach the star again and keep them up to 25 years old.