remember we make an arbitrary cut off at third as a country that comes third once beats a country that always comes fourth by most metrics

Indeed, and I think this is one of the strongest arguments for the IOC's lexicographic ranking being a more natural one than the USA's total-medals-first approach; in the IOC scheme, the fact that medals stop at bronze has the effect of making the list less precise (sets of countries which would have been contiguous in the rankings now become equal), but in the USA scheme the arbitrary cutoff after third place is actually critical to what order the countries end up in.

Yes, that's interesting, and I think it makes sense. It may or may not be fair, but it's certainly more consistent :)