What troubles me more about the sequence is the fact that even after 15 years and a major refit, they hadn't changed the codes. Of course, the need to change passwords is more apparent to us now in this age of multiple passwords and identity theft then it was in 1983. Even so, it seems at the very least the codes would have been changed after "Let That Be Your Last Battlefield" seeing as everyone on the bridge got to hear not only the codes, but the abort code as well.
OTOH, it was a nice little nod to continuity in the movie. And watching the two scenes gives a very interesting contrast -- in LTBYLB, it was part of a calculated power play for control of the ship -- while Kirk was aware of the risk, and I believe would have done it (as duty required), you could see he was playing up the situation to intimidate Bele. Kirk was aiming for gaining control, not destroying the ship. In TSFS, this instead was a struggle to "turn death into a fighting chance to live" There was no plan of retaining the ship or getting the Klingons to back down. Kirk wasn't bluffing or playing a game of "space chicken" to come out ahead. He knew he WAS destroying the ship for real, and that really came through in each of the actors' performances.