When some say "I laughed so loud I literally rolled on the floor", they do not, in any way, mean "I laughed so loud I figuratively rolled on the floor". Instead they mean "I laughed so loud, that it was almost like I was literally rolling on the floor". It is merely used as a generic augmentative: the phrase has the same basic meaning with or without "literally", but it gains more emphasis with it. The fact that it happens to apply to a figurative usage of "rolling on the floor" is mostly a coincidence.
Its just like "very" (which is a contraction of "verily", truly) has been adopted as an augmentative and lost its original meaning of "truly".
But no one uses ‘using “literally” to mean “figuratively”’ to literally mean ‘using “literally” to mean “figuratively”’, either. Instead they mean ‘using “literally” in the context of a figurative usage’, as you point out—the censure of which is warranted by its being a lazy cliché. The augmentation is not generic; the coincidence is feigned in the service of irony.
Lots of people do use literally, which manifests by them complaining that it is becoming a self-antonym or that it's losing its meaning. Is it a lazy cliche? Probably. Is that a reason to complain it's hurting the word literally? Obviously not.
Several words in English have multiple separate meanings.
> people say "break" when they mean "brake".
You were still able to understand what they meant.
Rather, instead of "should we accept", I'd ask "can people be expected to understand".
I'd think a divergence in language is more severe if it disrupts communication.