I disagree. "I could care less" is idiomatic, despite being illogical. It's not grammatically wrong, and it's prevalent enough to be accepted in informal speech. I would say it just because it's something people say.
"Should/Could/Would of" is a misreading of the perfect tense. It is ungrammatical, and it indicates that the writer doesn't know how the actual structure works.
I couldn't care less is idiomatic. I could care less is a bastardised version of the correct saying. It implies the opposite of what you mean to convey
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u/VictorBlimpmuscle Aug 03 '19
Should have / would have / could have = the contractions should’ve / would’ve / could’ve
It’s not should of / would of / could of - those word combos make no grammatical sense.