But they do keep a Constitution
as a museum piece - and she's not the E-A, as her bridge apparently is of the late 2260s standard still. Also, she's the only one.
Unless I'm reading too much into "Relics", that is. Picard waltzes in on Scotty's simulation and recognizes it for Constitution
class, which is fine, because we never saw the TOS design associated with the bridge of any other class. And then he says there's a Constitution
class in the museum. Doesn't mean Picard recognized the simulation because it was identical to the museum piece - he could have recognized it because visuals from the 2260s adventures of various Constitutions
were part of the public consciousness for some reason or another.