This sort of thing has already been discussed to death in the past. There is simply no way to implement any of these without creating a "bring this or get stonewalled" situation that nobody wants to deal with.
The number one selling point of this game has always been the ability to bring whatever and roll. Tossing that aside to "encourage" (read: FORCE) certain team comps is a good way to guarantee your new mission/TF/whathaveyou collects dust. You brought up LGTF - almost nobody plays it, even when it's the weekly. Barracuda is another one with AT-based gimmicks - again nobody touches it.
It's past time to put down the square peg instead of continuing to try and force it into the round hole.