BOAC, what you suggest makes sense from an aerodynamical point of view; prevent the plane from trimming itself into a corner from where it's hard to escape. I would suggest to limit the trim to the point where full TOGA power can be given and the plane can be kept under control at stall-speeds and attitudes. (One of the issues that played in this accident is that the 737-NG engines can overpower its controls.)
When you limit trim, it would mean an Autopilot disconnect too; forcing the crew to take action... Would not have made much difference for BA038, where the crew (intuitively) was aware of problems (and with their engines they were incapable to GA). For Turkish 1951 it could have made a 200-300 foot (and some knots airspeed) difference to make a go around.
Putting up my system engineering hat; it certainly is possible to add "underspeed protection" or "overtrim protection" to an autopilot. It adds to complexity, introducing a new failure mode into the automation. (Consider inappropriate activation of the protection mechanism.) Should manual trim be allowed to override the protection?