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.
OTOH, she may have been made a showpiece, and later be the source of the apparent Constitution
class wreckage scoped in BoBW...