It is sometimes (often even) discussed directly, but being cross-correlated to these proxies means that there are different perspectives on what the operative or underlying essence is.

Part of the definition of class that is often overlooked in discussions is that it's not just about money. This is why the socio qualifier gets added into the "socio-economic" designation... even though people sometimes use the dash and then ignore it.

A class implies a hereditary, cultural and quasi-ethnic aspect. So does caste, obviously.