Trim tab location

I've noticed that a lot of aircraft put trim tabs on the trailing
edges of the normal movable control surfaces. Wouldn't this just
deflect the control surface to neutralize the forces and not affect
much change except drag? It seems like you'd want to put the trim tab
on the fixed part of the wing/stab/vert, that way its pushing the
airplane instead of the flight controls in your hands. I've noticed
some articulated mechanisims on some aircraft (anti-servo) but this
seems to be a complicated way to make up for the fact that the tab was
put in the wrong place to begin with. What am I missing?