The players no doubt will be paying fee's to their agents above and beyond what you see the club announce as their agent fee's. Plus all that'll happen if you forced it all onto the players, and this already happens anyway, is the players will just demand a payment the equivalent to that of the fee's so they are paid, and this would be more expensive for the club in the long run.
it is a lot more complicated in reality think.
players pay agents fees based on their contracts - so percentage of signing fees, wages, mage rights, commercial deals, etc.
then there are expenses related to arranging transfers and contract negotiations. the club will incur fees that are reported as transfer fees that relate to transfers. these will involve facilitation, contract negotiations, etc. most are related to legal fees and the like. but there remains an element that seems murky, and relates to facilitating deals. so often clubs seem to deal significantly with particular agents. this is largely opportunistic (get to know the agent, get to know his player's agent, get to know the player's needs and plans first.
there is always going to be an element of duplicity as a result. and possibly it is an area of the game that does need to be looked at for purposes of clarity. cos firstly there is a ALOT of money involved. and secondly because there is vested interest in clubs being involved with agents, agents getting involved with clubs, relationships that service agents and directors more greatly than it serves players and clubs, and ultimately fans.