We had an old pioneer sound system which had a big volume knob. You could turn it by hand but if you used the remote it would turn when you turned volume up and down. Possibly these are similar where they automatically tune and turn but allow for manual interaction in case of emergency.

For the sake of external consistency, seeking a problem to fit the solution:

It seems like there's relatively little on the ship in the way of rotational mechanics, doors make a pneumatic sound, etc. Perhaps the equipment is highly EM sensitive? Like the electromagnetic waves from a motor could screw then up somehow kinda like electrostatic issues in a computer?

In a post-scarcity society, they let you have the job you want. Those knobs don’t even do anything but they make him feel like an integral part of the ship's operation.

I have some thoughts on that despite the fact that I don't even watch the show.

For the first point: Load distribution to ensure that the system wears down more evenly is a thing that can be done. Yeah you may be able to automate it but there can be reasons why you may not want to do that, like added complexity that makes the system even more failure prone For the second point: It's still a lot easier to maintain something than it is to fix it when it's broken. Having eyes there to do that may just be a way to get someone to check for potential failure points before they become a problem. Even if they may be in other systems nearby that are unrelated. Having someone check those systems by hand also has a security aspect to it because it makes it less likely that someone can just tamper with that system. Yes you have dedicated security personnel but security is still everyone's responsibility.

Also. Plot points and all that stuff that makes it fun to watch.

I think it's a joke

They don’t, Rutherford just likes the acoustic nature of it.

My theory was always that they're not supposed to overheat unless rotated they're supposed to distribute heat evenly through some internal mechanism. They don't really work properly and an upgrade was developed that improved heat loading.

This necessitated some redesign of the interface.

But because they're in an old California class the interface was never replaced with the newer model, and so they are still stuck with the old capacitors. Given the fact that the California class is not a frontline vessel, at least it's not supposed to be, and is unlikely to be far from a space dock, it was not considered a major issue to have them running on an old system. Also the California classes are physically relatively small vessels, so perhaps the plasma load isn't enough for it to matter anyway.

Alternative theory: it's a Cali class ship, so the EPS capacitors did rotate automatically once over the course of a day, but that system broke and they haven't gotten whatever replacement part is required, so they put ensigns on the task until the automated solution is fixed.

As to the second, typically automation is a balance between complexity and use of the automation vs difficulty and time consumed by a task, which is to say that if you only need to do a task like change how the capacitors are wearing in once a year or more, and it’s relatively safe and easy to do by hand, then it just may not be worth the trouble of automating be having someone do it by hand every now and then.

We had an old pioneer sound system which had a big volume knob. You could turn it by hand but if you used the remote it would turn when you turned volume up and down. Possibly these are similar where they automatically tune and turn but allow for manual interaction in case of emergency.