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... and then the site proceeds to work just fine with cookies blocked.

In my experience it's become that or "Open these sections and select 'No' on every item, meaning it'll be 20 more clicks before you can see the content of this page"

That is not compliant with GDPR anyway.

Appreciate that you now know they absolutely despise their users and take action by never using that site again.

The cookie warnings are not about GDPR.

The cookie warnings are not a consequence of the GDPR (remember they've been there before) and also only need to be done when you have non-essential cookies on your site (i.e. tracking, ads)