Why bother with an asteroid? If you're able to get into Earth orbit, just go the rest of the way and slam into the planet. Or do what they did in the B5 spinoff...which I think was called Crusader or something (I don't care enough to Google it) and poison the planet. Sisko was able to cobble something together on the run on the Defiant
to poison a Maquis planet, so I'm sure the Breen could do the same to Earth with some planning.
Anyway, as we later hear the Founder promised Earth to the Breen as part of joining the war on the Dominion's side so the Breen are going to be a bit reluctant to blow it up before they even get the keys to the planet.