Do many people really say "I could care less" instead of "couldn't"? I've never heard anyone say it, and the few times I've seen it used online the perpetrator has rightly been rounded upon.
If people do, what similar turns of phrase would they likewise mangle? "Well done son, I could be more proud", or "I'm completely thrilled, I could be happier", or "I'm at rock bottom, things could be worse".
Yes, I've definitely heard it many times. Unlike the other examples you suggest, I think it's become common enough to begin to be a semantic unit, whose meaning is not perceived to be a function of its parts.
If people do, what similar turns of phrase would they likewise mangle? "Well done son, I could be more proud", or "I'm completely thrilled, I could be happier", or "I'm at rock bottom, things could be worse".