You think most new authors have wealthy families?
That is a very odd assumption, given how hard it is to write a book... and given how low the returns are... and given how many other ways there are to achieve prestige... and given how little people regard authorship these days as a measurement of it... and given how unlikely it would be for wealth to have an outsized representation in a career generally associated with poverty... and how all old authors were once new authors which would imply that most of them are wealthy too, which, not so.
Further, to address your own point, they are not even the representation of successful authors. There's thousands and thousands of successful authors that aren't even near to being close to the gates of the Western canon.
In the 20th century, there have been hundred of thousands to a million different titles published. If even 10% of those authors made enough money to be considered a living wage, it absolutely dwarfs the number of authors in the cannon, which is on the scale of 100s, not thousands.
If the cannon is your standard, your standard excludes almost the entire industry.
It is worth pointing out that there's nothing particular odd if it were the case that writing was subsidized by wealthy families. For the vast majority of the history of writing, writing was subsidized an left to monks, philosophers or aristocrats. It's only been in the relatively recent time period that writing was a potential occupation for anyone interested with enough skills/talent.
Anyone trying to make any amount of money at writing writes genre fic of one sort or another. Fantasy or maybe sci fi, and probably "juvenile fiction" (tends to sell better to adults, too). Romance (which may or may not actually be straight-up porn, basically). Airport thrillers. Not lit-fic. Never, if your goal is to make any money at all.
And yeah, the publishing-side heavily favors people with money, lit-fic or not, for the reason that making a living at it requires excellent connections to get you directly into a high-paying part of it, or else years and years making less than it takes to live on in places like New York, to work your way up the ladder. Either way, that probably means family money. This phenomenon been mentioned, directly or obliquely, in IIRC all of: Bullshit Jobs (Graeber, 2018), Fussell's Class (1983), and The Official Preppy Handbook (Birnbach et al, 1980).
I know a guy, for example, that worked two years in his spare time on one game, got picked up by a publisher, ended up in Barnes and Noble and was considered a success by the publisher (they even requested and released an expansion), and the guy got only $9,000 in royalties (with no advance) for all his efforts.
Pretty much the only people making enough money for it to be their sole form of income are either hired directly a publisher or are out there hustling constantly and signing like 8+ game designs a year, or have insanely cheap cost of living (one game designer mentioned how he made net income of $12k one year and was able to survive off that because they live super cheaply), or have somehow landed on a massive evergreen hit, like Azul or Carcassonne.
[1] https://twitter.com/JPacCantin/status/1647455444884156417