In TOS we know from a line that there were onlly a dozen or ships of that class. Of which we know for certain one under went a refit and 3 were lost in service. Leaving 8 or so unaccounted for. Sure the Enterprise might have been the most famous ship of that class but Starfleet could have determined that the class as whole from the TOS era had served with distinction and decided to preserve one of the other 8 as it appeared in the TOS era.
That just doesn't make any sense to me, I guess. I don't think there was anything special about the original version of the Constitution-class other than Kirk's ship was one during his five-year mission. Sure, we can speculate that every
Constitution-class ship was special or noteworthy, but that still wouldn't preclude the ship in the Museum being a later version of the design, though.