I think it would be initially better, then gradually become worse. And that's a horrible thing when the public is concerned.
There's still people out there concerned about the "memory effect" for battery charging, and recommending a full discharge every time, even though that advice has been obsolete for decades now due to different battery chemistries. But the public easily latches on simple advice and doesn't consider the technical reasons for it.
So I imagine the same would be the case here. You'd have a marginal improvement for a short time, until the situation changes and suddenly people have to absorb "Yes, this was fine in 2023, but now is a complete no-go in 2026".
Since we're considering UX here. What UX do you propose that would reliably tell my nigh computer illiterate mom what to do with "the self-signed certificate for this site changed" if she receives it at a hotel while traveling? And what if she first opens the site in a hotel abroad, then comes back home and gets it there? How are non-experts supposed to untangle that?