I don't know about a Trick Room ability being broken, but the potential to over-centralise battling is certainly there. It would be "safe" to use the slowest stuff possible, or run something that can counter Trick Room (if such a thing comes into existence). It would completely change the look of competitive battling.
However, is that actually a bad thing? As much as one pokémon / ability / move forcing the game to move around it sounds ludicrous, in reality all this would do is make people more inclined to run slower pokémon. It has potential to centralise in the same way needing to be fast centralises now, and I never really see people complaining about teams needing to either be fast or have priority moves.
I mean, considering Stealth Rock (a move that renders multiple types of pokémon unfavourable to unplayable) is legal, I'm not sure an ability that swaps the direction of speed wars would be too bad.