This is one of those areas where I think it's about the complexity of the task. What I mean is, if you set codex to xhigh by default, you're wasting compute. IF you're setting it at xhigh when troubleshooting a complex memory bug or something, you're presumably more likely to get a quality response.

I think in general, medium ends up being the best all-purpose setting while high+ are good for single task deep-drive. Or at least that has been my experience so far. You can theoretically let with work longer on a harder task as well.

A lot appears to depend on the problem and problem domain unfortunately.

I've used max in problem sets as diverse as "troubleshooting Cyberpunk mods" and figuring out a race condition in a server backend. In those cases, it did a pretty good job of exhausting available data (finding all available logs, digging into lua files), and narrowing a bug that every other model failed to get.

I guess in some sense you have to know from the onset that it's a "hard problem". That in and of itself is subjective.