Any other comic could have told the same joke and everything would be just fine, because they would use a funny voice and become a "character."
I disagree. The problem is, it isn't a joke. A joke requires structure. What he said was post Season Three Family Guy humor, which is nothing more than a sentence.
I always think back to when Steve Irwin had just died tragically in a scuba incident with a stingray. Norm MacDonald was on the Daily Show and he made a few unbelievably poorly timed, but outrageously funny comments about Irwin's death. The key to it working was that he wasn't degrading the guy that had died (or in CK's case, the ones who suffered from the trauma of a school shooting). They were twisted observations about how anyone could be shocked that a guy named "The Crocodile Hunter" had died. Edgy comedy requires finesse and in general, the more tragic or complicated the subject, the more finesse and talent is required to pull it off. A good example is Life is Beautiful won an Oscar (should have won more) and Jerry Lewis's abomination (despite good intentions) is locked away in a vault.
So this isn't about the character or persona of the comedian. It is simply that CK Louis didn't even bother to try to make an actual joke. And that is why it wasn't funny. At the very least it is offensive to people paying money to see a comedy show, when a comedian phones in material.