I was all set to be mad, but took some time to think about it, and I'll concede the point.
I still think this interaction is annoying. I'd estimate that games "end" in around half as many turns as if this event wasn't on the board, and shorter games are naturally going to have more variance. The closest comparison is to Tournament. You can be more skillful in spiking the Province early, and still lose because you didn't draw Province with Tournament, or your Province was at the end of the shuffle. This is more extreme than that scenario, which already worries me. Note that even if you can't play Possession every turn, it's likely you can buy more Possession when playing with your opponent's deck, so even a soft Possession pin is hard to come back from.
PPE: KC-Bridge games actually are a crapshoot, but for different reasons. KC-KC-Bridge-Bridge-Bridge usually isn't how those games end. What happens is someone hits KC-Bridge, snowballs ridiculously, then hits KC-KC-draw-Bridge-Bridge for the 3 pile. So, you get a crazy first turn advantage. I see the point though.