Strip the cheese out and the piadina has to carry prosciutto crudo on its own, which changes what the bread is being asked to do. Here there is no soft fresh cheese to bridge the salt; the warm Romagnolo flatbread is the only counterweight to a cured, salty, faintly sweet ham. That is the whole logic of this build. The round comes off the hot plate blistered and still soft, and folded around the prosciutto it does two things at once: the warmth wakes the fat in the ham so it goes silky instead of waxy, and the plain, slightly fatty crumb dilutes the salt enough that slice after slice stays comfortable rather than punishing.
The craft is in the bread doing more work because it has fewer partners. The dough is flour, lard or oil, water, no real leavening, rolled thin and cooked dry on a screaming plate so it freckles dark and sets pliable, pulled before it stiffens into a cracker. It wants a touch more fat in the mix or a faint brush of oil so it stays supple enough to wrap a dry filling without shattering at the crease. The prosciutto is laid in loose ruffles, never pressed flat, so air stays in the fold and the ham does not compact into a salt slab. It is folded in half and eaten warm and immediately, while the heat is still in the crumb and the fat in the ham is still loose.
The near relatives change one element and stay regional. There is the version that adds squacquerone or stracchino to soften the salt, the one built on prosciutto cotto for a gentler, sweeter read, and the dressier fold with a few leaves of rocket and a shaving of grana for a bitter, nutty lift. Each is this same warm round with a single thing swapped, and each deserves its own article rather than being crowded in here.