Based on the article, only four particular streets are affected, and only during high-traffic times of the day. This could have the effect of spreading out the foot traffic to the major sites.
I have to hand it to the Mayor, though: it's far cheaper to pay one police officer to roam around handing out tickets that contribute to the city's bottom line than to install benches and garbage cans and then pay someone to maintain and empty them, with no added revenue. Also, in some parts of the world people use public garbage cans and mailboxes as impromptu urinals. This may not be the custom in Florence, however tourists do come there from all over the world, and no matter how often you empty the trash there will still be a major stench if someone uses a trash can that way. It's not something people will necessarily want in a historical part of the city. People who wish to be overwhelmed with stench can always go to Bourbon Street in New Orleans, Louisiana.