The problem with a push-off is that the muscle group you are using is less powerful and less easy to control than a conventional pull-off. There are times when a pull-off is very awkward (for example in Sor's Variations on a Theme of Mozart, where you are pulling off the second string but still leaving the first string vibrating), but my feeling is that for speed and power, a pull-off will still work more effectively, and the direction of the pull-off is easy to aim so that the higher string is missed. I'm not sure I could aim a push-off as accurately.
Hammering a non-vibrating string is not that uncommon - I can think of a few pieces where it's marked to do so. You're right - we need a massive toolbox of techniques we can draw on.
I find what's much more of a problem is stopping the strings I've plucked, or indeed those that join in with sympathetic vibration