Eating from sandwich shops

Eating on the streets is not forbidden, as long as you don't camp in proximity of major monuments such as cathedrals, palaces, statues etc.
This has nothing to do with the Italian custom of having a meal in a restaurant or in a closed place, but it's a matter of decorum.
You can have your lunch sitting on public benches, or you can eat gelato while walking, there's no problem in doing that.

I don't know where people hear this stuff and why they believe it, but Tobia is right: thousands of tourists camping any day, 18 hours a day in front of the same house in an 5 feet-wide alley... that's forbidden. Same for a neverending stream of tourists eating on stairs that are 300 years old while seagulls, boars and rats kindly wait for their shift.

Eating while walking is allowed, otherwise Ice Cream shops would go bankrupt and Sicilians would starve the moment they leave the Island!

Thank you Tobia and Dario for your responses.

I don't know where people hear this stuff and why they believe it,

As to where tourists get the idea, well news outlets such as this, whose title headline is: Italy's Florence Bans Eating in the Street

https://edition.cnn.com/travel/article/florence-street-eating-ban/index.html

seagulls, boars and rats kindly wait for their shift.

boars?

Yep, boars:

https://www.npr.org/2021/09/28/1041124299/wild-boars-rome-streets-food

As far as I know - and I could very easily be error - the pillaging porcine haven't made their way into the historic centers. Yet.

I knew that that wild boar ragu had a different flavour

tmalave - the mercado centrale, second floor, in Florence is great for a quick bite. It has seats, but its a food stall place where you order to go and sit at one of the table available. Quick and fun

https://edition.cnn.com/travel/article/florence-street-eating-ban/index.html

Well, I wouldn't trust any article beginning with "Italy might be the home of al fresco dining" Even if it was true, there are nicer ways to put it!

Anyway, in Florence and Rome they temporarily banned camping "on sidewalks, roadways and on the doorsteps of shops and houses" , not eating while walking.

As far as I know - and I could very easily be error - the pillaging porcine haven't made their way into the historic centers. Yet.

Sooner or later they will be back on the hills of Rome! The Gees are late, but the Sacred ducks are proudly marching to Capitoline Hill.

We are heading to Italy next week and I 100% need to eat gelato while I walk so that I can trick myself into the idea that I am burning calories. HAHA!

When traveling, we never plan any meals. And we've eaten all kinds of foods in Florence--including Chinese. There are a lot of street vendors in most Italian towns, most of which are serving decent pizza. And we like to eat gelato any time we can get it..

In Florence, we found Leonardo's to have great lasagne. It's close to the Duomo, and is an upstairs working class cafeteria.

Once you get there, you will observe how people eat on the streets.

There are two All'Antico Vinaio locations in Florence. The one location closer to the Uffizi usually has a line about a half hour long minimum. The other location, closer to the Accademia is way shorter. Same food, just shorter line.

Eating while walking is allowed, otherwise Ice Cream shops would go bankrupt and Sicilians would starve the moment they leave the Island!

A little dig at the folks from the southern island?

Hmmm...maybe things have changed, but part of our experience in 2015 of All'Antico was finding a place to sit and eat on the same street along with all the other people, making sure not to block merchants (who poured water in front of their entrances) and cleaning up after yourself. I think there is always a way to eat on a bench or the ground if you are polite and clean. For Gelato or any other snack we always managed to find a bench to people watch and enjoy our snack.

maybe it is