"Google doesn't care, and these other sites don't care, so why should I care?"
I have found that validation serves a very important purpose - to guide your development. I have lost count of the times I have encountered CSS with all sorts of extra junk because things didn't look right, and the reason for it was that the underlying HTML was invalid.
Yes, the browsers are smart. But they are still guessing. If you leave out a tag, the browser will close it for you. Not always in the right spot. Invalid pages could also result in a DOM tree that's not quite right, so JavaScript could be affected.
Developers should validate their pages just as they lint their code, to ensure quality.
Of course, if you're using cutting-edge elements, they won't validate. But that's a little different story. It's not a reason to not validate, it's just a reason to filter out those errors.