Since all the manufactures want to use superchargers they will be forced to handle payments properly (certificates on the car not a flaky payment terminal on the charger). Should help for third party chargers also.
BTW, CSS2 supports 3-phase AC charging, which is common in Europe, but not in the US. In this regard NACS would be a downgrade for Europeans.
But I'm not totally convinced Tesla is going over the cable rating. A lot goes into the rating of a particular cable -- everything from conductor material and size to the insulation around the conductors, proximity of conductors, etc. Not to mention the liquid cooling. It's plausible that supercharger cables are rated for more than 600A.
Not to say they are unsafe or anything but it’s not unheard of
Likely what will ship in the US is similar to the EU non-Tesla solution, where you just use their app.