I don't think that's true - AFAICT there's no EU law banning analytics. EU law just restricts storing & processing _personal_ data (GDPR) and storing unnecessary data on machines without consent (ePrivacy/'cookie law').

If you want to log fully anonymized data, without persistent tracking ids and without leaking personal data to 3rd parties en route (so no "send it to Google and they promise to anonymize the IP afterwards") then you're all good (but IANAL!).

The only reason you see all those cookie notices and GDPR consent requests is because so few companies are willing to accept even the tiniest tradeoff in their metrics to protect their users' privacy.