Eh. I'm in exactly the same group she's talking about (born in 84, so at the upper end of millennial age) and my inheritance has started already. My parents have calculated that they have enough to live on until the time they expect to die, so they're passing any extra onto me early to avoid inheritance tax.
Personally, it kinda grates on me. I'm very much a soft socialist, who believes in everybody paying their fair share of tax. I've also derived a lot of satisfaction over the years in becoming self-sufficient[1] and being able to pay my own way without them having to prop me up. But it's their money and they're free to do with it as they wish.
As it stands, I'm doing the privileged thing that the author mentions, and 'refusing' it: it's going in an investment account and I'll continue to live within the means that I earn myself. But I know that that still means that I'll never be afraid of having to live on the dole, or do a job that I utterly hate.
In any case, even without that money, as an ex-FAANG developer I'm still significantly more privileged than most of my peers: I don't have any debt, I own my (fairly cheap) home outright, and I own a (very cheap) car and motorbike, also outright. Amongst my friends, most of whom are renters working in precarious jobs, I just don't mention money.
[1] How does that work with the socialism? Well - I'm happy to take from the government, because everybody can get the same, and I've repaid that with taxes over the years.