Should pizza be firm enough to be held by the crust?
Speaking as an Italian, both Neapolitan-style pizza (thicker crust on the border) and rest-of-ITaly-style pizza will have a thin center that will normally bend when cut or held; the more so if there are lots of toppings. It shouldn't really disintegrate, that may be an indication of a bad knife, too.

Normally bending dough isn't a problem because you can fold the slice: