Nobody has yet defined how rich is rich. An income of £50,000, £100,000, £1 million. Must it be earned or inherited? How much capital makes someone rich? £1 million,£10 million? Do you have to be privately educated? It is difficult to discuss the undefined.
On the subject of developed potential and social. In the 19th century working men got together to form Mechanic's Institutes, Working men's clubs where ordinary working men thirsty for education would get the best teachers. The WEA, Ruskin College, Oxford and the extra mural departments that many universities used to have all sprang for this demand from working people for access to education. A significant number of miners sons (mainly) and other men of humble origins got to university like that. I went to a mainly engineering and science based university college in the 1960s and at least half the male students, including DH had working class background.
The question we need to ask now is why the more affluent classes who, previously were less interested in education became to keen on it and why those from working class back grounds have thrown away the culture of education and replaced it with a culture of being proud to be ignorant.