The main reason I prefer the "older ship" theory over "new ship shunted over to Kirk" one is the interiors of the E-A, with their GNDN tubes and TOS-style shuttlebay. We know some Constitutions
were subject to refitting; it just makes sense for the E-A to have been subject to it as well.
The secondary reason is that Starfleet could afford to give Kirk an older ship. If Starfleet felt it really needed newbuild Constitutions
in the 2280s, it would not part with one and sacrifice it as a means of keeping Kirk out of mischief.