I can't see anything wrong with double bridles.
Remeber, they have TWO reins, so if you just want to ride it as a snaffle, you can - there doesn't NEED to be any curb/leverage action brought into play at all
Not that there's anything wrong with that - the bit rein can be used to give far more subtle and complex cues. Compared to some of the leverage bits I've seen in other disciplines, the curb part of a double bridle is one of the gentlest things you can get.
Is it just the fact that there are two bits? I don't see an issue with that.