I don't know why anyone would be against this. It would provide a greater challenge, allowing the Elite 4 to be on higher levels.
Could water the game down, depending on how it's done. It would essentially force a Gym into nearly every city/town you enter, so it could cause the issues we saw in GSC where there was a a huge level jump between Kanto and Johto.
At least, that's what I can think of as to a reason why you wouldn't want this.
What if we could challenge the gym leaders at any time?
Every gym could be challenged at any time, similar to Mega Man? However, with Mega Man there was always a weakest robot master... however with pokemon you already have a type that is super effective to other types. There would be a way to play each of them depending on which starting pokemon you choose. Sort of like how Faulkner doesn't allow you to get electric pokemon... until after the gym battle.
Currently playing: Chrono Trigger (DS), Super Mario RPG (VC), Final Fantasy Tactics: WotL (PSP)