Not that I necessarily hate the notion... but why?
Think about it. There was nothing particularly significant about the Enterprise-A that we're aware of. She met something pretending to be God and saved the Khitomer talks. Psh. That's a slow day for the 1701-nil.
I would say that because it was commanded by Kirk, would be enough. He is sort of like that era's John Paul Jones or Admiral Nelson and considering the original 1701 was destroyed, and since it seems that the entire constitution class was retired and presumably mothballed, the real question is why would you mothball the 1701-A, when you don't have to?
Besides, it was mentioned that one of the NX ships (wasn't clear which one), according to Troi in These are the Voyages, was kept around as a museum ship, so it makes sense to me they might keep a constitution class ship around as a museum, too. And if they have to choose which one, well Enterprise-A would get it, at least in my world. I mean an Enterprise that DOESN'T get destroyed is a rare thing, so you best preserve one when it retires when you can!