> Prestige based on family lineage is considered a big deal
Are you in the UK? The monarchy and House of Lords are an obvious anachronism and they need abolishing [1], but I would say it's a very small minority who care who you parents are/were (mainly people who think their own parents are/were a big deal) — and a similar small minority who might also ask "which school did you go to?".
I suggest this exercise: Pick a random person from Queen Victoria's court. Look up where their descendants are today.
Chances are, they're still running the country in some capacity. (The example I'm thinking of was a Duchess. Her descendant was a beak at Eton who taught Boris and the haunted pencil).
People with Norman names wealthier than other Britons
People with "Norman" surnames like Darcy and Mandeville are still wealthier than the general population 1,000 years after their descendants conquered Britain, according to a study into social progress.
(Alec d'Urberville in "Tess of the d'Urbervilles" is a nouveau riche person who adopted the name rather than a descendent of the original d'Urbervilles. Probably that happens in real life, too, though I expect the people who did the study have taken that into account and have done the best they can in the absence of reliable public ancestry data.)
If you read that paper carefully (it's been a while so I might have this wrong), I think you'll see that while they're using Norman vs not-Norman surnames, the comparison is between Victorian and contemporary wealth and life expectancy data.
(Obviously the discrepancy has to start with the Conquest, I'm just saying that strictly speaking you can't use that paper to support that conclusion).
I don't think that's actually a fact. I don't know what figures you're using, but eyeballing the Global Social Mobility Index puts the UK as pretty middling in Europe. Less mobile than France or Germany, more so than Italy, Spain, or Poland.
If your point is the UK is just about in the lowest 50% of European countries by social mobility (keeping in mind Europe is pretty good on a global scale for social mobility), it's basically a non-point altogether. If the UK were at the end of the scale it might, but it's not, so it doesn't.
I think that if you look at the people in positions of control in political and economic sectors (and mass media, which is a key element), the vast majority came from just a few schools.
Are you in the UK? The monarchy and House of Lords are an obvious anachronism and they need abolishing [1], but I would say it's a very small minority who care who you parents are/were (mainly people who think their own parents are/were a big deal) — and a similar small minority who might also ask "which school did you go to?".
[1] e.g. https://www.sortitionfoundation.org/