Multiple goodies in this post.
I think your excellent first comments on violence and avoidance also touch on the ritualistic aspect of slapstick. Ritualism is not only repetition, but also culturally meaningful. I'd argue that slapstick does indeed require violence. This is not necessarily interpersonal violence, it could be one person against the elements (or a banana peel). Otherwise you've got "physical humor". Think of the moment in "Bringing Up Baby" when Katherine Hepburn tears her dress and Cary Grant helps her disguise it by welding himself to her back(side) and marching across the room with her.
Several of the moments leading up to the stroll are slapstick - tearing clothes etc. - but the actual walk across the room is just a sublime moment of physical comedy.
Second, slaptick doesn't go back only to commedia. There are traces that go back to our earliest Western drama - the Greeks circa 400BCE were swatting each other with phalluses. No doubt our caveman ancestors were miming club fights around the campfire.
Finally, I'd like to note that stunt performers refer to stunts as "gags", I presume because of the overlap with slapstick comedies. These share many of the qualities of true slapstick gags.