But I don't see how that extends to a flagship for the whole of Starfleet.
Indeed, I don't think the idea of a "flagship for the whole of Starfleet" is even meaningful. A flagship is the command ship ...
I don't think the Enterprise Dee was a flagship because it was a command ship, or carried a Admiral, rather it was the "Flagship of the Federation
" because it was a showpiece, a emblem of the Federation's prestige and a demonstration of it's abilities.
Businesses have flagship stores, much bigger than their standard outlets, possessing greater stocks of inventory, and often found in prestigious shopping districts.
Auto manufacturers have flagship cars. Like the Chevy Corvette, an expensive signature vehicle with looks and power. when Chevy displays a company commercial, the Corvette is prominently featured.
The Enterprise Dee as the "Flagship of the Federation
" is like those flagship stores and vehicles, large, powerful, and expensive. Starfleet, with the same materials and assets, could have built two or three medium sized starships that could have individually carried out most of the Enterprise Dee's missions, instead they built a "flying starbase."
And don't call me Surely.
Somebody had to do it.