In fact Rome is not the right place to understand what is pizza. You should go Naples. Keep in mind that Italy is made of a lot, really a lot of cultures. It is not the same to stay in Naples than in Rome. Naples was a Greek colony, Rome was an Etruscan colony.
If you are in Rome you can understand what is carbonara, matriciana, abbacchio, etc. If you ask for a pizza you are astray.
Although I agree with you I would take note that Naples being a Greek colony and Rome an Etruscan colony do not have much to do with differences in pizza matters. Those societies and the appearance of pizza have a couple of millenia between them.