Hbombers are far more powerful than any defensive naval unit you could add including loaded Carriers which are actually weak as they risk not just the navy but also a nations defensive airforce as well. 4-5 HBs can destroy just about any navy from my experience. It may cost a lot in terms of lost bombers, but these can be rebuilt lost bbs, Carriers, ftrs cannot.
I agree that the HB would severely restrict the movement of this Allied Navy, my only point being that it could be built without being sunk.
But how did the issue of HB come up? I guess you are assuming thats how the Allied (or Japanese) Navy is eliminated. HB (along with IT IMO) is almost always a sure win in the game for whichever nation has it.