Definitely Pyraminx by far. Then 2x2, 4x4, and Siamese, though unfortunately Siamese is not official.
IT SHOULD BE! I love siamese 3x3. The only puzzle that I have that I was able to solve all on my own (not counting of course the stuff i learned on 3x3, cuz I would've never figured it out otherwise)
For sure. The main problem is there isn't a mass produced one. There would be a lot of hidden mods (not necessarily a bad thing), and I'm sure plenty of them would break during competition.
They'd also have to create weird rules. Like would it be legal to solve both cubes at once with different hands, or one at a time? That changes a lot.