There are other places with a similar experience that don’t have the same oil wealth. I wonder though if it’s different at the higher end of things, like expensive treatments for major issues which a tighter public purse might not stretch to.

That's an asset, not a savings rate.

USA's mean household Net Worth is $500K more than Norway's, and average household is about 3 people (some households are single people) so the oil fund approximately cancels that out.

No, I don't think the oil fund (https://www.nbim.no/en/) is responsible for the culture to be on time or is connected directly to the public healthcare finances. Though being a state with money helps, obviously.

Perhaps you could explain how a fund that doesn't invest onshore does this. The government uses only a small percentage of the return on the fund (not the capital) each year.