Yes, Mollygo - and there are different reasons for different cities too.
I'd never go to Florence in the summer for example - when everywhere is packed out. Also, we tend to stay outside and come in for the archirecture, galleries and gardens. I am one of those visitors who likes to chat to locals, and try to live a bit like them for the three weeks or so of our trip.
We now have friendships with locals we re-visit when we holiday there - people who have welcomed us into their homes.
They are not like "home" friends but it's nice to have a catch up with them, learn to cook something new and learn about their way of life over the years.
The idea of the 3 cities is interesting though.
I wonder if everyone else (as I have done) wondered what criteria to apply?