I don't see why the Supremes are any different from other tires that have thin sidewalls that give a really beautiful ride quality.
Absolutely one has to be careful with a tire like this, but I don't think I'm overly lucky with the supreme 2in and 1.6in versions I've ridden a lot on. I would say that I've just used common sense with them and have ridden on lots of different surfaces, but the majority on pavement.
Touch wood but so far, I've never really damaged a tire over the last 30+ years of riding pretty regularly.
Touch wood again, just for good measure!