The Mountain Mike’s pizza in my hometown used to do that certain night(s) of the week when I was a kid. I don’t know if they still do.

Similar dynamic, they’d come out with a fresh pizza, do a lap around the dining room, and if you wanted that flavor you’d ask for a slice, or keep waiting.

I don’t remember if adults could make requests / suggestions.

the only 'rodizio' I've seen in the US tend to be on the higher end, while most all you can eat pizza places tend to be on the lower end and just self serve.

There is a place in Texas that does this called Delucca, I've been to their Dallas location and really liked it.