as you say, class discussions remain mostly on a superiority basis. It’s simply a term and doesn’t actually relate to specific networks, private or otherwise.
Classes were originally developed to describe large routable networks on the internet and the most common classes were grouped in the a, b, and c derivatives that we’ve all heard of.
So as long as the sizing is held, then classful networks can be implemented and utilised. I’ve seen a class A 5.0.0.0/8 private network implemented and a 192.168.0.0/16 network, all appropriate, all working fine. Not very well, admittedly, but possible.
Cisco in particular used to drive this style of networking. Make a huge, big, flat network. Create a strong shell around it and then just create this crazily huge switched network with a single default gateway out the front door.
you’ll not see things like that any more.