I heard a lot about social mobility watching the Republican convention last week, none of it very analytical. I think it's helpful to take this issue out of the context of partisan politics and think about a totally different situation. The "feudal" society portrayed in George R.R. Martin's Song of Fire and Ice Books (on television as Game of Thrones) is a good example since it has a simplified class structure. Some people are landed aristocrats, and some landed aristocrats are owed fealty by lesser lords. One guy is the king.
We can see pretty quickly that the extent and nature of social mobility in this society is going to be a demographic question rather than a public policy question.
We're told in the text that before the start of the books, the continent was ruled for a few hundred years by the Targaryen dynasty which was able to enforce its hegemony due to the possession of superweapons in the form of dragons. That's a recipe for peace, and we can see from the lengthy lineages of the noble houses that the kind of wholesale eradication of a house that we see during the wars portrayed in the books was rare during the era of peace. Meanwhile we know that Westeros is wracked by severe and unpredictable winters that lead to food shortages and widespread hunger. It stands to reason that in those conditions, death will disproportionately afflict low status families who'll have less ability to command scarce food resources. Consequently, Targaryen Westeros is going to be a society of persistent downward mobility. Due to starvation and disease many poor peasant fathers will leave no sons, and many noble fathers will leave more than one son. Consequently, at any given time a reasonable share of the smallfolk will be the (possibly illegitimate) grandchildren or great-grandchildern of lords and very few lords will be the grandchildren of commoners.
This calculus shifts during wartime. Lords are expected to command forces in person, and slaughter of noble families is the only way to wipe out their claim to the land. Under situations such as these "vacant" lands will become available for assignment to lower-born persons of merit such as Peter Baelish and Davos Seaworth.
UC Davis economic historian Gregory Clark argues that England in the era before the industrial revolution was like Targaryen Westeros in this regard and that it's important. Systematic downward mobility allowed for the population-wide diffusion of the habits (literacy, for example) and genetic attributes of high-status individuals. Consequently over time the quality of English human capital was rising leading eventually to the industrial revolution. The United States—as noted by not properly explained by GOP convention speakers—is the reverse thanks to immigration. We're constantly adding people at the low end, so the aggregate trajectory is upward.