There's one song that has that phrase that I think you're okay with, Word Crimes by Weird Al:

Like "I could care less", that means you do care, at least a little

THANK YOU! I don't fucking get this at all. "I could care less." ..... So you care a bit? What?! This is so dumb.

I could care less

The person is actually threatening to care less than the status quo, when the other is asking them to care more.

On the other hand, people that tend to use that phrase probably aren't even thinking of any meaning (whether it is the correct or incorrect one)

it's weird because i could care less implies that you have a base level of knowledge that you wish you didn't have. But it also means that you could also just, care less than you currently do now, i hate that phrase.

This is one of the few times I can't help myself. I become that guy instantly.

"OH SO YOU DO CARE!?!? SO YOU COULD CARE LESS BECAUSE YOU DO CARE!?!?!? GOT 'EM!!"

Weird Al got upset enough at this that he put it in a song:

I hate these word crimes
Like I could care less
That means you do care
At least a little

https://www.youtube.com/watch?v=8Gv0H-vPoDc

(I'm really glad he did that parody because I find the tune really catchy and the original song is rapey.)

I literally posted the exact opposite thing, here it is:

The phrase “I could care less” makes more sense than “I couldn’t care less.” They’re both idioms and therefore are both considered correct linguistically speaking.

But “I could care less” indicates you would prefer to not have to care about a subject so is expressing that you’d prefer to stop talking about it.

“I couldn’t care less” doesn’t indicate the current level of caring so you might say “there isn’t anything in the world that will make me stop caring about my children; I couldn’t care less about my children.” Without the idiom those aren’t contradictory. It’s only because of the idiom there’s an assumption the reason the person can’t care less is because they don’t care at all. But nothing about the phrase indicates this.

The level of concern for something with the phrase “I could care less” is indicated by context and the phrase indicates whatever someone may have assumed about one’s concern from the context is actually more than the person actual concern for it.

But people will often say “I couldn’t care less” is better than “I could care less”. They’re wrong and I could care less about their wrong opinions on idioms.