First all the managers here "suffer" wage grow at the end of the season anyway so if the players work that way so can the trainer
Except, of course, the players' wages grow (or shrink) because of the changes in their skills. A trainer level 4 today is a trainer level 4 next season and a trainer level 4 until the day he dies - no skill increase possible to make him more valuable and therefore in need of more salary, and no deterioration of skill with age to provide a reason to replace the trainer. Having a big salary increase slotted the first week of each season will just mean that everyone will have to scramble to replace their staff at the same time as everyone else, leading to ridiculous bid wars or the inability for anyone without a padded bank account to have a decent training staff at any time early in the season.
The current system at least allows you to spend a little or a lot and to budget your spending - if you have a lot of money up front, you can buy a better trainer starting with a lower wage. Or you can buy a trainer with a worse starting wage and pay less up front, but then you'll feel the difference week over week. Or you can decide that you don't want to spend the money at all and just roll with a lesser trainer, or in the case of PR managers, switch between a basic PR manager with Crowd Involvement and one with National Appeal depending on where your next game is.
The idea of taking a fixed percentage of weekly income is one that's an interesting attempt to try something different, but removes pretty much all decision from the player - the option to run with lower level staff is gone, because you're still paying a premium price. Instead, it becomes a race to go ahead and save up the money to buy your level 7 trainer and level 7 doctor, knowing that once you shell out whatever it costs to acquire them, you'll have them forever at the same low percentage of your income that a level 2 staff member would cost.