> If you have to hold USD to buy and sell USD products (as a European)

Approximately no individual does this. Some companies may hold some foreign currency reserves, but even there it is not _particularly_ common in most cases.

As a European, I have never, in 40 years, had any USD, except a small amount of paper currency. If I'm buying something made in the US, I'm probably buying from a local vendor, or else will convert on the fly. If I'm visiting the US, I'll convert on the fly (this is even cheap, now, thanks to neo-banks). I own a bunch of US equity, but indirectly via a euro-denominated global market index fund. This is fairly standard. In general it's only common for individuals to hold foreign currency where the local currency is particularly unstable.