This seems subtle to me. The following seems fine to me as either formal or informal usage:
He was loud as Jupiter, proud as a terrier.
I think the reason this doesn't seem informal to me is because I invented it as an example in a pretentious poetic style. On the other hand, this seems clearly like a colloquialism:
He's dumb as dirt.
One of your examples:
If they were dumb as him, we would have a bigger mess in our hands.
This doesn't sound to me like natural speech by a native speaker. On the other hand, this seems fine to me, but again pretentious and poetic:
If they were loud as Jupiter, we would ignore them still.
A side issue with "as him" is that in formal grammar, this should be "as he," but that would not fit at all with the style of the rest of the sentence. You can also say "as he is," which is correct in formal grammar but doesn't call attention to its own formality.