To say that a TPA is necessary when two respected and legitimate managers become involved in a bid war is ludicrous.
I am going to guess that the TPA exists because of inexperienced managers. If an experienced manager knowingly overbids on a player, something more than a TPA should happen. Also, please attempt to not twist this into the same thing. An educated manager investing a large sum into a future star is not the same as a new one falling victim to a lame starting transfer price.