Yes it should. Kind of in the same way that it should be "I couldn't care less" instead of "I could care less" which I've seen a lot more in recent years.
Literally just talking about that! I agree that the original intent (and, you know, meanings of words) should make it "couldn't" but I think the two have linguistically drifted together within the phrase.
The rules-boy in me rallies against it, but the descriptivist in me celebrates and I couldn't care less how he said it.
On a slightly more serious note, it makes dry humor a bit harder to land since you can't rely on subtlety as much. Like "I could care less about my SO" in context where it's the punchline of a misdirection joke.