I think the use of the delta fleetwide might have to do with its iconic status in pop culture. I bet as many or more people can identify the Star Trek delta than can identify the symbol of the Rebel Alliance. So I think the movie retconned this symbol to be the Starfleet symbol and not the Enterprise symbol. It's similar to the manner in which the 80s movies adopted the Enterprise symbol for all Starfleet. I don't think it had anything to do with the Enterprise in particular, although that was an attractive in universe explanation. I think it was just a practical realization that for many viewers, casual and otherwise, the delta is synonymous with Star Trek.