Care less? Or less care?

For the second time this week I have seen, in professional writing, the phrase "could care less."

If one could care less, that implies that, to some degree, one does care.

The idiomatic expression that describes a complete lack of interest is "could not care less." Which is to say that one doesn't care at all, so it is not possible to care any less.

I bring this up because I could not care more about the proper use of our language.