In these various elevator algorithms, it's not commonly discussed the overall wear and tear on the elevator. More movements would typically translate to faster repair times. Hydraulic fluids needing to be replaced, parts breaking, etc.

Efficient elevator algorithms will often suggest moving an elevator into a preempted positioning strategy, based on time of day or peer elevator positions. The scheduler might move an elevator up to offset one coming down, for example. The demand-signal algorithms at least minimize movement in this way.

I think minimizing maintenance at the cost of increasing wait times is probably an important balance to get right. No doubt, the cost owners for maintenance are not going to perceive the wait time of passengers to be as important.

Not to mention maintenance means taking an elevator out of service, meaning average wait times go up during that period.