I remember Picard barking out commands to make the ship do preprogrammed evasion or fight maneuvers too. This seems like another good use.
(Also worth noting is that "pre-programmed evasion patterns" are used in normal circumstances, too. "Evasive maneuver JohnDoe Alpha Three" works just as well when spoken to the helm officer as to a computer. I still don't know whether such preprogrammed maneuvers make sense in real-life setting, though.)
But specifically manoeuvres, rather than weapons systems? Today, I doubt it: the ships are too slow for human brains to be the limiting factor. But if we had an impulse drive and inertial dampers (in the Trek sense rather than "shock absorbers"), then manoeuvres would also necessarily be automated.
In the board game Star Fleet Battles (based on a mix of TOS, TAS, and WW2 naval warfare), one of the (far too many*) options is "Erratic Manoeuvres", for which the lore is a combination of sudden acceleration and unpredictable changes in course.
As we live in a universe where the speed of light appears to be a fundamental limit, if we had spaceships pointing lasers at each other and those ships could perform such erratic manoeuvres as compatible with the lore of the show about how fast they can move and accelerate, performing such manoeuvres manually would be effective when the ships are separated by light seconds. But if the combatants are separated by "only" 3000 km, then it has to be fully automated because human nerve impulses from your brain to your finger are not fast enough to be useful.
* The instructions are shaped like pseudocode for a moderately complex video game, but published 10-20 years before home computers were big enough for the rule book. So it has rules for boarding parties, and the Tholian web, and minefields, and that one time in the animated series where the Klingons had a stasis field generator…