I mean, fair enough. It's reasonable to assume the something trashed the ship between then and 2401 where the ship looks nice but isn't space-worthy anymore, at least not for what its designed to do.Perhaps the Defiant-A was messed up by the Prodigy shenanigans, and it became cost effective (In terms of the 24th Century), Besides it has been 25 years since the end of the Dominion War, the Defiant-A did other things too. If we go by your logic, why even have museum ships, it is not like tactile contact is even a thing in the 24th Century.
Now this had me thinking... If the Ent-D remained in service for an entire year after the brief-return of the Borg, why can't we just have 2 Enterprises cruising around the galaxy, the Ent-D and the Ent-G?