You have described, accurately if glibly, the situation in the West prior to the Industrial Revolution and globalization, which have brought world-historical growth in economic, educational, and spiritual quality-of-life for non-elites.
Over the past ~150 years, our society has been remade; higher education is hardly the esoteric province of the aristocracy and clergy it was ~700 years ago in Europe, and as you imagine it will "obviously" soon again be.
There's no doubt the elite retain advantages of birth. Perfect meritocracy seems at odds with humans' intuitive creation of entrenched hierarchy and autonomic drive to empower and extend one's specific genetic legacy. But even when beset by imperfection, corruption, hypocrisy, etc, a Western non-elite human's life is not likely to turn out "solitary, poor, nasty, brutish, and short," as is it would have in almost any other age. A peasant in Lancashire c. 1350 could reasonably bet many of his children would die, and those that did not would live almost entirely the same life as his own. A working-class American can make the opposite bets just as reasonably.
All this to say: I'm no Whig historian, but it is impossible to deny tangible and massive improvements in the average human's access to education and general quality of life over the past several generations. It is therefore absurd to make "obvious" predictions such as you have, contrary to a pervasive, macro trend, without providing some insightful analysis. (William Gibson's Cassandra cries should not be used as primary evidence...)
We rich, lucky ones, likely as not great-grandchildren of semi-literate factory peons, seem, generally, to exist in a cynical milieu which thoughtlessly assumes inevitable dystopia (an anti-Whig history!). But recent negative trends in, for instance, the Gini co-efficient, are minuscule vibrations within a relentlessly positive curve [https://ourworldindata.org/income-inequality].