Does closing claude code do something that running /clear does not?

Yeah, it re-sends all the agent system prompts.

Any clue why you might be a favored/favoured high value user?

The entire conversation is fed in as context effectively compounding your token usage over the course of a session. Sessions are most efficient when used for one task only.

I get a decent amount of work in before restarts.

Pro is 20x less than Max