MIMF

Why is the pivot block under the tail piece necessary on archtops but not on violins or cellos??

It's not necessary, at least on the archtops I have made or worked on, which includes some very high end instruments.

The violin family use a gut or nylon cord that bends easily like a hinge. My bass has a braided stainless steel cable loop. I've seen some busted hinges on guitars and banjos, especially the cast ones.

As long as you seat it properly on the tailblock, nothing wrong with using a raised violin-style saddle as the fulcrum for the sacconi. I preferred it to the inelegant (& spruce-denting) pivot glued to the tailpiece underside. But that's just me.

After thinking on this I can see where a bone or ebony block would lessen the chance of gut breaking and I can see it as protection when metal cable is used but why a fulcrum block as well, on the under side of the tail ala Benedetto ? Does it have something to do with tone or holding the tail in place maybe?

???
Regardless, you need something very hard for the cable to "break" (in the "break angle" sense of the word) over .... otherwise it will dig it's own groove.

By "raising" that something (ie making the saddle higher, like a violin), you lift the tailpiece high enough that you don't need the underside piece to maintain clearance from the top.

makes sense Dave thanks