I'd argue that the millionaire's / millionaires' wealth denotes a situation of true ownership, thus only the anti-apostrophe lobby would countenance dropping the apostrophe (and note that the apostrophe disambiguates here). With writers guilds and dogs homes (and especially working mens clubs in the UK), the apostrophe is often dropped. See Is it correct to say that I write children books {not-possessive case}?

Law professors might know law, but they don't necessarily know language that well. Apart from anything else, as @EdwinAshworth points out, with no apostrophe we don't know whether he's talking about the wealth of one millionaire or several / all. I don't think the fact that we often don't include any apostrophe (or pluralising "s") in forms like User / Users / User's / Users' Guide excuses the cited usage. To me, it just looks ignorant (better would have been the singular "noun adjunct" form millionaire wealth if he didn't want to include any apostrophes).

'The social status of the intellectual' extends the same meaning to any intellectual or to all intellectuals. But the Saxon possessive requires an apostrophe as @FumbleFingers states in order to define number.

@FF I seem to remember that there's at least one articulate contributor here who's an apostrophe abolitionist. Perhaps the prof is in the same camp.

A law for the Yale professoriate, a law for those of us who would write English. Take your pick, but only one of them is acceptable to me.

@David Did you boycott Waterstone's/Waterstones when they dropped their apostrophe?

@EdwinAshworth — I go there for coffee with Italian-speaking friends on Fridays when our classes aren’t running. I haven’t noticed any apostrophes in the coffee before or since, although it’s been a while because of the pandemic.

@David 'A [single] law for those of us who would write English' is hopelessly idealistic. There are those who say << mens >> is unacceptable. But most working mens clubs reject it for this associative usage.

@EdwinAshworth — Non-native speakers asking if it’s ’OK’ to break rules that are difficult to learn in the hope someone will say yes, reminds me of the agony Aunt columns of my youth where countless girls would ask if it was ‘OK’ to let their boyfriends… Perhaps I am an agony Aunt, always saying no. But returning to Waterstones (they can call it what they like) we did actually boycott it for a while when they changed the furniture in their coffee shop. Found an alternative run by a friendly Italian-speaking Albanian. Probably didn’t use the subjunctive — it’s a class thing in Italy.

Can you cite the author/source? It would be shocking to me if this were anything other than an editorial error. Note the economic conservatism in the first point... doubt this guy is an apostrophe progressive.

When I first read "The millionaires wealth does not cause the paupers poverty. I read it as poverty to the paupers similarly to The tax didn't cause the villagers [any] distress, not "the paupers' poverty", and then thought huh?

@cruthers This is from near the end of Chapter 4 in “Slouching towards Gomorrah” by Robert H. Bork. In his book he used Americans’ many times with the apostrophe. So yes, editorial errors may be an explanation…

@DjinTonic This actually makes sense. In that sentence perhaps millionaires wealth doesn’t necessarily need to be the wealth owned by millionaires but the wealth attributed to millionaires (and the like)…

But then “the intellectuals or the societies social status” may be more questionable even if he means attribution instead of possession because I have never heard of “children or adults book” or “men and women club” as a non-native speaker… (?)

But anyway I guess from the comments it’s fairly safe to say this is at least not a conventional usage in modern English, right?