I've worked at a couple of theaters where the floor is treated as sacred -- it seems most common in very old theaters where they want to preserve the history of the building or something. But I've also worked at more than a few where the stage is absolutely part of the set and is often painted.
We joke sometimes that the stage, at this point, is more paint than wood. Consider that we do around 6 MainStage shows a season, and each show is at LEAST one coat of paint, probably more. That's 6-12 layers of paint per season, and the last time we stripped the floor was around 2000 … it's a lot of paint.
Every so often something will happen (a piece of equipment might catch and gouge up a bit of paint or peel it back) and it's like the rings on a tree. You can look at the colors and count back shows.
We've been discussing stripping it again. It's only been done once since our current stage was built, but it's getting to be about time again.