One possibility. The bridge in IV is actually an auxiliary control room because they found the actual bridge (the V bridge) needed some work which Kirk and Scotty thought they could do on the way to wherever. Then they found they couldn't and went back.
Realistically, this is silly. They would not have left Spacedock with a barely functional bridge.
In the TNG Technical Manual, Mike Okuda's explanation for the change between TVH and TFF was that the bridge was a detachable module that could be swapped. That explanation
almost works. Almost. The only part that doesn't is: why would the bridge module be swapped out so quickly?
The only two explanations I can come up with that make sense here are:
1) The bridge was destroyed in a battle between TVH and TFF. Possible, but if things got to that point, then a lot more would've been damaged too. So highly unlikely.
2) The Enterprise-A really did start off as another ship, like fan theories have suggested, and it wasn't brand-new. Then it was decided to replace the bridge, which was already scheduled to happen anyway, with or without Kirk, registration change or not.
In the end, though, I agree. These are
all silly explanations to cover over the set needing to be replaced and William Shatner wanting the bridge to have a new look while they were at it.
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Anyway, Kirk and TWOK. Aging and dealing with being middle-aged is an important theme to TWOK and I understand that. But I get a kick out of Kirk saying he feels "old and worn out" at 50, considering that William Shatner is 95 now! And in pretty good shape for 95.