Not a bad idea, in theory, but... suppose I visit a site on Monday and see certificate A. Then when I return on Tuesday, I see a different certificate B. What reason is there to think that A is likely to be the "true" certificate, and B isn't?
Showing a big scary warning in one case, and not in the user, implies to the user that the browser has some reason to think one is more secure, which is misleading.
Showing a big scary warning in one case, and not in the user, implies to the user that the browser has some reason to think one is more secure, which is misleading.