It's would be interesting to see how the best crazyhouse players could handle not opening theory !
Also the other variants could be played with random piece setup. Horde, 3-check, King of the hill ...
In all the variants there are some standard attacks already. Without them play could be much more interesting.
It would be good, but I feel mixing variants would get a bit complicated sometimes. Crazyhouse is intimidating enough for most beginner players (I know I get wrecked in under 10 moves in tournaments sometimes).
Variants are not popular enough to multiply them at this moment.