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.