If you have to setup a company today, and want the easiest path to EU-wide SaaS, probably Estonia is the way to go, very easy for EU citizens (don't know how the experience would be from outside, if it's even possible).
Too bad that Estonia won't exist after 2027...Russia will gobble it up alongside Latvia and Lithuania.
It seems easy enough for US residents as well: https://www.e-resident.gov.ee/nomadvisa/
Checking the requirements, it seems to me that any "first world" citizen would encounter a low barrier for entry, with exceptions for Russians ("second world" citizens).