I believe Pisa at the time was part of the Duchy of Milan (a constituent state of the HRE) which at the time was under Spanish control (previously under French rule).
My personal bet is that it has something to do with many lords with conflicting interests(Pope, King of spain(?), emperor and the duke). This left some people unattended and free to experiment all kinds of weird stuff.
Also the Genoa and Venice seem to have played a big role. I think this relates to how they based their economies on naval power, but had strategically very bad positions. So they had to stay ahead in technology. (Byzantine empire on the other hand controlled the most important choke point in European trade at the moment. So they had no such need to innovate.)
If that were the case "Italy" would have taken the place of "Spain" and Portugal at that time regarding seatrade and clearly they didn't neither then nor in the future being almost irrelevant.
Power shifts, Spanish empire got upper hand in Atlantic trade. But they could capitalize on already superior technology of Europe against their colonial vassals. So no such pressure for innovation.