My government's websites require solving a reCAPTCHA for basic services, which is horrifying. They also use Cloudflare which blocks me sometimes. This is in the EU
Confirming this. I am also completely certain that gratuitous CAPTCHA use is banned for government systems by my country's set of laws governing their implementation. The judicial system and the community have not matured enough to consider this a breach of law worthy of fighting against...
reCAPTCHA (and others based outside of EU) is illegal on privacy ground (in any site, not just owned by EU entities). Homebrew CAPTCHAs are illegal due to their general lack of accessibility (in any site owned by an EU entity), and in Bulgaria their gratuitous use is banned in government sites on account of them being poor UX (not enforced unless caught during the acceptance phase of a project).
An example of an inaccessible homebrew CAPTCHA that causes very poor UX can be found on the portal that provides access to the legal acts of the Bulgarian judicial system: https://legalacts.justice.bg/ . Try taking the legal system to court. I tried for this one, you can see for yourself how it went.