It's likely true that it's fallen, because inflation affects people further down the quintiles more than people at upper quintiles, and directly reduces class mobility. That said, just looking at how the GSMI is scored, it appears that they aren't outcome-focused, and instead look at correlative factors like educational access (which is tied to cost of education) and health metrics which drags down the US against its peers. By sheer outcomes, the US is in the top 3 most socially mobile countries in the world.
This is really not true anymore. We have fallen significantly down the list, especially if you look at our economic and political peers.
https://en.wikipedia.org/wiki/Global_Social_Mobility_Index https://www3.weforum.org/docs/Global_Social_Mobility_Report....