That's basically what Blizzard is doing in 5.4. Not necessarily by battlegroup (those pretty much don't exist anymore), but they're merging many servers together with the Virtual Realms system.
Although, even if you merged all of the servers in a battlegroup together, it wouldn't make BGs and LFD same-realm under the current system. Those aren't limited by battlegroup, but by region (US/EU/Asia).
it'd be nice if servers didnt exist anymore and there was just 1. i hope that the virtual realms eventually does this. although i guess it would remove the revenue from server transfers...