My pet theory was always that the Enterprise-A was built from 'spare parts' left over from the Constituion refit cycle, similar to the space shuttle Endeavour. It's based on nothing but supposition, of course. A pulled-from-mothballs Constitution about to be retired works too. I think we all know the Yorktown tale from Gene comes from the Enterprise originally being called Yorktown in his initial treatments.
I like this theory. Works well with the Enterprise-A being a glitchy mess in STV.