> > - started in single user mode or with system indices disabled? > why?
Some of these I suggested just as a datapoint (or other brainstorms I couldn't immediately reject). A cluster where someone has UPDATED pg_* (even pg_statistic) or otherwise hacked on I would tend to think about differently than a "pristine" cluster that's never seen anything more interesting than a join.
How about "has run in a state where system catalog modifications are permitted". Because I've had one seriously frustrating case where that would've been extremely pertinent information.
That said, I'm not convinced it's worth the effort and I think this is going off into the weeds a little. Lets focus on Andres's core suggestion (and maybe refine the fsync part to get rid of false positives due to bulk loading) and build on from there in subsequent work.