Florence does get gridlocked in the summer. The historic center really isn't designed for vehicle and pedestrian traffic with any kind of volume - and the city has chosen to prioritize pedestrians. That said, it wouldn't shock me even a little if the cab companies did contract out a bunch of capacity to a convention. Pitti Uomo usually has transportation arranged, though - shuttle busses and such. The fact that taxis became easy to get when the convention was over isn't necessarily evidence that taxis weren't taking public fares, though - if traffic is the issue, the traffic itself also ends with the convention. The truth is probably somewhere in between, though.

Uber would help Florence a bit, primarily for folks staying outside of the inner ZTL, but anything inside would be an issue absent a taxi license (or a personal residence permit). You'd still have to walk up near the train station, past l'Accademia or down toward Porta Romana outside the ZTL to grab it, though. Ironically, Uber would have been of most help to the area around Pitti Uomo, which is just outside of the ZTL at Fortezza da Basso.

The traffic up by SMN sucks, too. You could very well get in a cab out front and sit there trying to leave the station on a normal day. I'm not trying to blame the tourists for staying in the wrong place because it's really hard to know this unless someone tells you in advance, but during the summer months, you really do need to stay in walking distance of the things you want to do.