It makes more sense to call it the Eton system. Oxbridge is accessible for many smart young people, but in itself that does not invite you to the political elite. It's Eton and a couple of other schools.

Pretty much any male politician whose official actions could be described as inhuman or sociopathic has been through boarding school trauma.

I think we are mostly on the same page. Elite universities are fine in a industrial society because you are more limited by physical resources. South Korea does relatively well being run by relatively few rich families. Because it only takes so many executive, managers or engineers to run factories refining natural resource. An elite university can produce the people necessary to fill those slots.

In a post-industrial society, or beyond that, you aren't tied to physical resource in the same way. Instead you are limited by the amount of people with relevant knowledge. The existence of elite universities in such a society is really more saying that you can't produce enough people and opportunities.

Arriving at a village finding there is only one person with a car you don't say "wow, this guy is successful" you say "ouch, this is a poor village" even if that is the most successful person in the village. Because these days we expect cars and if everyone had cars he wouldn't stand out as successful.

NB, in current UK English "matriculation" describes the process whereby the student is formally enrolled by the university. It is a formality and happens after they arrive at the university but before they are taught anything. A matriculation photo is taken by the college at the beginning of the first term. That is all there is to it.