Has anyone done anything like this for historical time periods? I realize the data is inherently sparse, but I'd be curious to see what the results would look like in 1900, 1800, 1700, 1600, etc.

My impression of the data is that, actually, we're doing pretty well with social mobility. Not perfectly by any means, and there is lots of room to improve. But as compared to (I think) just about any historical period, I think the graphs would be even more skewed. I'm fairly certain that as a medieval peasant, there were basically no viable routes to improving your lot (and even the word "lot" betrays the assumptions of the time), and so acceptance was the only viable route (violent rebellions excepted).