It's not the ship that's being honored, it's Kirk, the first time around.
Now we're ditched. Do we prefer an Enterprise
-centric vision for Star Trek or a Kirk-centric one?
(Personally, I go with the first since I've heard only good things about either Captain April or Pike)
Wouldn't explain NCC-1305-E, though, unless Captain Okita got given a replica of his old starship, too.
In my world, the prefix "13" would indicate a Baton Rouge Class starship, possibly suceeded by a sister ship of the TOS Enterprise, NCC-1305(-B).
Here is my try to rationalize the registry inconsistency in TNG:
WORF: Captain, there's another vessel approaching in sector zero nine one, mark two six.
PICARD: On screen. Magnify.
RIKER: It's a Federation ship. NCC 1305-E. It's the Yamato, our sister ship.
WESLEY: The Yamato's nowhere near this quadrant.
(WORF is growling.
RIKER: Lieutenant, what's your problem?
WORF: Family history. One of my ancestors served aboard a Klingon ship destroyed by the original Yamato in this war.
RIKER: Their war, not yours!
PICARD: Number One? (getting close to Riker) I suggest that we henceforth exclusively use the other NCC registry.)
Worf's (never revealed) later reaction to the destruction of the Yamato