There's a pretty good argument to be made that in the current MLB setup, most of the player development is really a result of the analytics and Player Dev departments, which aren't really based on one coach but rather an overall organizational philosophy. So it would really not only eliminate one of the more annoying pieces of the game, but also make it more realistic to just set overall budgets for hitting development, pitching development, and fielding development and call it a day rather than having to hire an individual person for each role. Set those three departments from $0-10M each or whatever and adjust the overall budgets accordingly.
We're not hiring individual team trainers or doctors. There's no real reason to do it with coaches other than "that's the way we've always done it" which is not usually a great reason to keep doing things.