I've made decent pizza dough using only salt, water, olive oil, yeast, and just a pinch of sugar to give some "food" for the yeast to use. Commercial pizza shops may add some sugar to their dough but I suspect they also add it to their tomato sauce.

Italians (and Argentines and Uruguayans by extension) make a pizza-type food called "fainá," using chick pea flour. Might make an interesting pie.

Fainá - estilo uruguayo

Fainá or Farinata