I believe this is mostly a cultural difference between Muay Thai and Boxing / Kickboxing. Muay Thai values continuous advancement forward and strongly views any backward motion as defensive. The bouncing back and forth is seen as weak and overly defensive in Muay Thai. But it works in boxing, because in boxing the emphasis is on scoring a point, rather than not looking weak.
You're not going to see rapid bouncing very much in Muay Thai, either, because it looks frantic and weak to Muay Thai people.
There's also something to be said for the fact that boxing doesn't have to worry about long-distance kicks coming at the worst time in that bounce. With Muay Thai, a kick can come very fast and strong, and if you're up in the air at the time, you will be knocked over or worse. Being knocked over in Muay Thai has a greater influence on judges than in boxing.
You will see this in kickboxing, though. And that could be because kickboxing is highly influenced by boxing. Whereas Muay Thai is much less influenced by boxing and has their own history behind the way it strikes.
That's it as far as I can tell. On the one hand, I think there's no reason why you shouldn't be able to use the bounce step in Muay Thai, but if it's seen as weak, maybe that actually matters. It's considered bad practice, so you probably shouldn't do it in Muay Thai.
Hope that helps.