Couple of points to add.
The downwards lift generated by the tailplane obviously also generates induced drag. Aircraft that are loaded towards the aft limit will be less stable (as stated) but will also have less induced drag and are thus more fuel efficient. Aircraft such as the A380 (I think - not quite sure) automatically transfer fuel aft when the onboard 'puters sense that the aircraft is in a stable cruise and on autopilot, and automatically transfer fuel forward when the aircraft starts its descent to land. All in an effort to reduce induced drag.
Furthermore, it is possible to have the tailplane providing positive lift instead of negative, but in order to maintain the stabilizing effect, this only works if the angle of incidence is lower than the angle of incidence of the main wings. Or something along those lines. It's a very tricky balance and obviously the CofG has to be just right to do so.