"United States does rank below the UK in terms of social mobility."

It always did, because the US had slaves, and ex-slaves who had no much opportunity to 'climb'.

The US now also has a giant class of a specific kind of migrant - Latinos from Central America, who are completely different than those from Spain or Cuba and the rest of the world. They exist in a kind of 'separate' USA and while technically might have the opportunities others have, they live in a system that is not suited to exploiting them. They are happy in their version of he US, they're family oriented, patriots - but not going to college or after the white collar trades like migrants from 'everywhere else'.

Those two cohorts make the US 'very different' in terms of social mobility, and so you have a situation a bit akin to Brazil etc..

Canada and Australia are 'Immigrant States' without those cohorts, and newcomers do reasonably well or somewhere approaching 'normal' after one or two generations.

I'll bet social mobility among non-African American and Latino Americans, is about on part with Canada or Australia, and maybe even a little bit better than UK, and most of Europe (even Sweden) which also have vestiges of class.

Some indicative data here [1]. You can see mobility gap between Black and White in the US, it's very crude and subject to interpretation, but it does line up with PISA standardized testing results which show the same, that non-Black/Latino America is actually 'a lot like' Europe or Japan in terms of so many outcomes. 2018 PISA test scores here [2] (download the PDF).

FYI I'm not 'endorsing' or 'supporting' any kind of system here, just pointing out that the the US has a 'multi system dynamic' different than other places and it's essential to understanding how it works esp. on a comparative basis. FYI a lot of E/S European countries are poor, and represent similar kind of 'isolated communities' which is why gini coefficient etc. for the entirety of the EU is much worse than it is for any individual EU state.

From 1922 until today - most of our progress has been incremental. Other than satellites, and maybe computers, it seems as though they ave predicted a lot. Maybe not quite the social impact of them however.

What will change in 2122?

If we have successful Fusion at scale, it could change a lot of things.

If not, maybe it won't be that different: longer lives, more fashion. Maybe we figure out Climate Change and get plastics out of he ocean, but we'll probably still be arguing about 'what is normal'

Eventually, we'll be able to colour our skin, eyes, hair very readily, we'll have cosmetic limbs (i.e. pair of wings that don't to much but flap a bit).
And maybe mechanical uterus - where you provide the eggs and sperm and it will make a baby in 9 months. If the identity wars are a bit complicated now just wait.

We will send a probe to Alpha Centuari and they'll be a small station on Mars, but it will be boring and young people won't even care.

Reduced population in the West and massive population booms in Africa and some other spots will crate some odd international dynamics. Africa will be much better off, but mostly still corrupt with crackpot leaders and nuclear weapons. One of them will use one on their neighbouring country.

[1] https://www.brookings.edu/blog/up-front/2019/02/14/no-room-a...

[2] https://www.oecd.org/pisa/publications/pisa-2018-results.htm