Nah, there are a bajillion ways of making pizza in Italy, it’s just that the thick and soft one is never round, but even the round one can be thicker or thinner depending on the local preference. It would actually be interesting to find out if the American style of pizza was influenced by a traditional Sicilian pizza called “sfincione” which is still very popular, given the strong Sicilian component of Italian immigration in the US.
On the other hand, Italian pizza can be too thin. For me, I like a crust that is thin but still has a soft inside with that lovely bread taste.
But only a fool would be searching for something other than true Chicago pizza to begin with!