The nut material can make a big difference, as can the width of the slots.
Binding can occur because the slots are too tight. As @Bill said, you can use graphite. You can use powered teflon. I have been known to pop the string out of the slot and fold a piece of very fine sand-paper into a V and slide it through the slot once or twice, then retrying the whammy bar. Repeating that eventually gets the nut slot opened enough to avoid binding. BUT, you have to be careful to not make the slot deeper; You only want it a tiny bit wider.
You can replace the nut with various materials, like teflon, which should reduce the problem a lot. See your local guitar tech about that.
You can replace the nut with a roller-nut, which has little rollers under the strings as they cross the nut. Again, your tech is the man to see.
As far as people doing some radical tremolo-bar work, watch the videos of Jeff Beck using his Strat for things like "Somewhere over the Rainbow", from his induction to the hall of fame. He plays entire parts of the melody using only the tremolo. Of course, after the song he might hand it off to his tech, but if he was suffering from out-of-tunedness, it would hit immediately after using the tremolo. So, even on a Strat it's possible to do what you want.