The sites themselves disagree with you. They think there's risk, which is why they decided to not work in the EU. EU does not "threaten very high fines" to sites that do not collect PII. GDPR does nothing if you don't collect information. But they obviously do collect it, despite your denial.
Of course the site owners think there it introduces unnecessary risks for them, that was more or less what my initial comment was about.
> But they obviously do collect it, despite your denial.
How? are you somehow compelled to share you name and address with random local/small new-sites from the US
They very likely are just using ads and/or analytics services which technically don’t comply with GDPR..
How else than technically should they comply with the GDPR? Morally? They don't do that either. They gather as much as possible and deduce as much as possible from it. Are you actually claiming services like Google Analytics aren't interested in knowing much about a site's visitors?