Opinions are going to differ. IMHO this is not too fast a pace. My preference is for at least 3 days in larger cities (which leaves 2.5 after transportation) and you're doing that. About transportation time -- a plan for 4 nites in Florence really means 3.5 days because the morning you leave Venice it will be lunchtime or later by the time you get there, get to the hotel, etc.
As for time per city, a lot depends on what you want to do; see just the city, or see some of the surrounding area too? If the latter I'd add on another day or two. My starting preference for 3 days means 1.5 days to see the city itself (walk around, a few hours at museums, etc) and then another day to either see nearby areas or spend more time exploring the city.
You'll enjoy the 3 nites in the Amalfi region; it is beautiful and relaxing (depending on how much you do!). If anything since it will take at least 1/2 a day to get their from Florence I would add a day to Sorrento and take one away from Rome or Florence. I suggest Sorrento as a base for that region over Positano since it is both easier to reach coming from the North, and more centrally located. The weather is uncertain that time of year and I'd make a set of plans so you can play it by ear. Among possible activities would be a day trip to Capri, a bus ride down the Amalfi coast, going to Pompeii or Herculaneum to see the ruins, a day at the beach, or just relaxing in town.