with the D gone there would have to be a new flagship.
Why wait for the E-E to be completed? There would be plenty of already existing ships to assume that role immediately. And no tradition of ships named Enterprise
holding the status!
If anything, some other Galaxy
class ship would be the natural successor, as that sort of hardware is known to be capable of the task. The Sovereign
class would not have demonstrated the capability yet. (And may indeed lack it altogether for all we know.)