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uBlock Origin actually has a blocklist for cookie warnings. It would still allow sites to function normally without the constant interruptions.

See "EasyList Cookie". https://easylist.to/

Or if you prefer to block social media junk too (as I do), Fanboy's Annoyance list includes both cookies and social blocking.

That's a bit broken for me now. I don't see the popups but I still sometimes get the overlays that stop me scrolling and I have to turn off ublock for the site, click accept, and turn ublock back on.

Grab the Remove Sticky bookmarklet to take care of that (not my website): https://alisdair.mcdiarmid.org/kill-sticky-headers/

Yeah, the only problem is that sometimes it is not clear that a site is broken, when just some parts are omitted, like a search bar.

And this is why the consent information/opt-in/out boxes ought to be able to run with JS disabled, too. It's easy enough to do that... but that easy if it's something that gets put on the site via JS.