Well, you don't haveto start with all of the powers if you don't want to.
Also, that is a little interesting, but this pokemon isn't going to have that much power over the worlds colliding. It's just there (along with others) to help seal the worlds and return them to their natural states.
Well, there are technically two special things about the pokemon, but only one is obvious (besides the fact that it is shiny)
1. Hydreigon could be special since it has three heads and perhaps each of the three heads is a world (or representing a world) OR, each of the three heads represent emotions and they are the thing that made the worlds collide in the first place/they are the ones that sent us on the journey to save the worlds colliding (although I feel that the last one is a bit of a stretch).
Haxorus and Heatmor is probably going to be the same as the last two reasons, or that they have a special ability that could make each world stop colliding...The last one could be the same for Hydreigon too.