Rather than say that each ship in the TOS era was supposed to have a different symbol (but production errors, realities and choices voided this idea and now require us to squint and pretend a lot), we could say that each Fleet or other sub-organization within Starfleet had a symbol of its own.
The 1st Fleet, the most prestigious one, would have the delta shield on the personnel operating its ships and installations, as well as possibly on the flag officers on Earth involved in operating that Fleet. Other Fleets would have the insignia seen on other TOS starships (as quite possibly there would be only one or two Constitutions per Fleet) but the ships docked at SB 11 would mostly come from the same Fleet as the Enterprise and would thus sport the same symbol in "Court Martial".
It would then be a relatively logical transition from many to one if Starfleet adopted the symbol of its 1st Fleet at some point - far preferable to the idea of them adopting the symbol of a single ship. After all,
a) Enterprise personnel never uniquely sported the delta
b) The delta is a fairly common symbol in real history and extremely unlikely to have been dedicated to a single vessel at any point
c) ENT nicely supports the idea that the delta saw general use just before the UFP Starfleet was founded
d) The upcoming movie will no doubt establish the broad use of the delta during Kirk's early years
e) We never learn that the Enterprise prior to TMP would have done anything so noteworthy as to deserve to have her symbol adopted as the general Starfleet logo.
Timo Saloniemi