You can get a trim tab that "works" but doesn't "stay" in position (one of the walk-around checks on a small plane it to set the trim max in one direction, make sure it moves correctly when you move the stabilator, set in the other direction, recheck) but you can't reach them on a large jet.

There have been cases where the ONLY thing working on the tail was the trim tab, the yoke cables broke - you can land a plane with only the trim if you really need to.