Yes we have an obvious class structure, but we also have upward mobility. One of the founders of Intel was a Hungarian immigrant. Bill and Hilary Clinton had humble beginnings.
The problem with this idea is that there is no internal coherency or intrinsic relationship between members of so-called 'classes'. Blurry boundaries, which makes the concept a convenient short-hand, but a fallacy for the most part. Every individual has a different combination of capital and market-skills, which is why we see upward and downward mobility.
It's true that any community forms a kind of hierarchy, with more poor people than rich, but that's exactly what you'd expect in any community, at any point in history. Wealth is rare and hard to come by.
Wealthy school districts with high property taxes have better schools than poor areas. That is a fact. If not class distinctions based on money we can invent a new term.
I can tell you when Hugh Hefner was alive I was not likely to get invited to the Playboy Bunny Ranch. Athletes and Hollowed actors were.
I dare say an average Brit is not going to hang out with te royals.
Over here there are no hard boundaries like the British royals, but the boundaries are there.
You might pay $20 for a meal at a regular restaurant. A more exclusive restaurant might charge $200 to keep out the social
undesirables'. Exclusive golf clubs.
For a long time in the USA loans to start a small business have been available to regular people. Upward mobility.
I'd say capitalism in the west has been reframed.