While we can speculate on what the 'dramatic' purpose was, the actual real life production purpose is that they wanted to make the Lexington's bridge look different than the Enterprise's... the same reason they changed the screen panels above the communications and science stations to make them different than the Enterprise's.
...which eventually doesn't make a lot of sense if the very next episode produced right after "The Ultimate Computer" features another scene on a starship bridge (i.e. Exeter
). Why didn't they make Captain Tracey's command chair higher as well?
Where the distinction explanation undoubtedly works is the very first time we see the bridge of another starship in TOS, i.e. the ISS Enterprise
from "Mirror, Mirror".
Since three starship bridges with three starship captains commanding (Enterprise, Exeter, Defiant
) featured the short command chairs, we have inevitably to conclude IMHO that either only starship bridges where a Commodore is the commander feature the high chair (we never saw the Constellation's
) - this would leave Wesley to be the commander of the Lexington
the chair is made higher once a flag officer assumes (temporarily) command of such a starship (however, doesn't work for Commodore Stocker in "The Deadly Years").
As a thought experiment, consider this: Had Wesley decided to conduct the M-5 war games aboard the Enterprise
, what would have happened to Captain Kirk?
Would he have just relieved Sulu and take over his place for the duration of the mission? Frankly, I find myself having a hard time imagining this for Kirk - or a supposed original captain of the Lexington