I assume that -p is the same that "codex exec".

The difference is that in this case the agent loop is executed, which has all the caching and behaviour guarantees. What I assume OpenClaw is doing is calling the endpoint directly while retaining its own "agent logic" so it doesn't follow whatever conventions is the backend expecting.

How important is that difference, I can't say, but aside the cost factor I assume Google doesn't want to subsidize agents that aren't theirs and in some way "the competition".