It's not banning 2 stages? If you want to see it that way then it's temporarily banning 2 neutrals for the first match only, but each player gets 2 "bans" so it evens out anyways. It's effectively a controlled random pick, and I think it adds an even deeper layer of strategy then the normal system does.
For example, take this wholly realistic scenario: A ROB player is up against a GaW player, and knows that they don't stand much of a chance on Battlefield. Winning that first match is very important, because that means you will be able to pick the stage for the last game of the set, if necessary. So, the ROB player decides that he must ban Battlefield in order to win. He does so, but then gets Yoshis, which is just as bad and loses because of a random factor that the players had no control over.
Now if stage striking were in place, the ROB could've stricken Battlefield and Yoshis, and the GaW could've stricken FD and Smashville, giving us a nice stage to Brawl on: Lylat. Which has its ups and downs for both, making it the most balanced stage that we could really get from a round 1 match.
Just because Brawl is full of random factors (****ing tripping, Olimar's Pikmin, Frigate's Stage flipping, etc.) doesn't mean we should be promoting even more of them. I don't see any problems with stage striking, really.