That said, I've never had a problem using it from the US.
There are complex laws governing residency which vary country-by-country. It's not atypical that, for example, if you spend 183 days in a year somewhere else, you're no longer a resident.
You're generally only a resident in one country. This governs taxation -- taxes are primarily based on residency, with some caveats. As a US citizen living in the EU, you will not pay the same US taxes as you would if you were living in the US, and in many cases, zero taxes.
However, as the other poster pointed out, from the perspective of a tech vendor, understanding the difference between:
- EU resident
- EU resident using a VPN in the US
- EU resident traveling in the US
- EU non-resident living in the US
For each request which comes in is practically intractable.
GDPR is also framed as a basic, universal human rights law. That also can have unintended tentacles. If you don't want a liability hole, it makes sense to honor GDPR for everyone, in practice (even if not under your ToS).
Practically, that's what everyone does. I've never had a GDPR request declined on the basis of residency (the last qualification being important).