Have you contacted C3 about it? They'll send you a replacement baseplate.
I've had a pair of Union bindings for 2 seasons now and have never had a problem the square logo coming off. You have a legitimate argument- I would also be pissed to pay $200 for a pair of bindings just to have a piece come off on day 1.
it's not right, and it is not
a "common" problem. I've never even heard of this issue before. You make sure you do everything you can to get this problem fixed. Call C3 via phone- that's the fastest way to get it sorted out.
And don't listen to Mr. Extremo over there. He's just an absolute Union fanboy to the point where if there's a problem (even if Union admits it), he'll blame the person who owns the bindings and accuse them of using them incorrectly or some other bullshit. He's done this on countless other threads.
I'm a fan of Union myself, but I don't try to praise them as being completely flawless. There have definitely been some problems with them now and in the past that Union has also acknowledged, and they're fixing all of them for next season.
Hope it works out for you!