Kilominx isn't nearly as luck-heavy as those other events. How frequently do you see stuff like a one-move layer? That's right, the answer is

*basically never*, even if you're full CN. (Back-of-the-envelope calculation says it's around 1/31000, which is less than the probability of getting a 4-move 222 scramble (1/1989), a 7-move skewb scramble (1/9.8), a 6-move pyra scramble (1/414), a ≤9-move Redi scramble (1/4365), or a one-move cross on 3×3×3 (1/1987), and also pretty close to a full cross skip on 3×3×3 (~1/32000).)

It's analogous to a 2×2×2 in the sense that it has only corners. It is absolutely

*not* analogous in the sense that it has a small state space, which it doesn't: the state space is much smaller than a megaminx's, sure, but still a few orders of magnitude larger than a 3×3×3's.

I know jack about the edge-turning puzzles (i.e. I might be very wrong here) but it honestly wouldn't seem too difficult to come up with a scrambler. Just do it like a square-1: pick a random shape according to the Markov steady-state distribution, then fill in the pieces, and finally solve and invert.

… And then I did a bit of searching and found

this TP thread about enumerating the possible shapes, and (i) it seems very nontrivial (unlike a square-1, which doesn't jumble) and (ii) it seems to be mechanism-dependent (see also Jaap's Puzzle Page's note about

how you might be able to force a technically-illegal turn through on the Curvy Copter). Also, it might suffer from the opposite problem of lolscrambles: with "proper" scrambling (whatever "proper" means), you can occasionally get shapes that are much more difficult than usual to solve. (Kinda like how, on a square-1, kite-square is a really annoying shape to deal with for people who are still using beginner cubeshape methods? Except that a Curvy Copter has so many different shapes that it's not realistic for anyone to just learn them all.)

(This is all very interesting and I am now compelled to get a Curvy Copter for myself.)