The middle class thinks in terms of money. Their personal status is not secure. You don’t know quite what car you’re going to get, what school you’ll be able to afford.
If you have your entire society operating with a middle class brain you’ll have a society that feels itself under threat all the time. A strong social climber mentality but not really on the ladders that matter—mainly on signalling ladders. It’ll be a society that does not think in terms of whole of society advancement, but rather in terms of personal advancement.
An actually good elite system is based on privilege. You have some people who don’t have to worry about their personal standing. And they are able therefore to use that position to worry about society. They are trained to worry on behalf of society.