The original argument was that seeing error messages often will make users ignore them, but I don't think certificate errors should be very common now. Either way, I think we should be encouraging users to read error messages more carefully. Maybe the Yes/No buttons on the dialog should be put in a random order, and the question randomly flips between "Do you want to proceed?" and "Do you want to abort?"... adding a "learn more" option would be a good idea too.
And since the former is (sadly) pretty common, this only teaches people that these warnings are not that unusual, and can safely be overridden.
It would be much better to have one "the server admin forgot to renew his certificate" type of warning and another "a totalitarian regime is trying to spy on you" type of warning...
And moreover, your scenario is essentially "worst case: fall back to previous behavior." That's not too bad...
And I think you can currently get certs expiring later than the domain, which seems wrong to me. Is there a good justification for that?