Not only is it impolite, you will get wet.
When I was there a couple of weeks ago (at night) the steps were actually not accessible due to a large rope around the area, but there was still 2-3 people sitting on the steps. I was bummed because I love to sit there and people watch. Water on the curb is used by merchants in Florence located close to the All'Antico Vinaio sandwich shop to keep people from sitting and eating sandwiches blocking access to their stores, no worries just keep moving down the street and you can find a dry curb, usually in front of a wall that is between stores. The sandwich was so delicious, we are still talking about it.
Have some respect ... have a picnic in a piazza ...not on church steps
Agree with Jim. It's a Catherdral and a major tourist site with a narrow entryway compared to demand for entrance. Don't sit on the steps.
Some piazze are historical sites, too.
The key word is "moving" - lots of people eat on the go, while walking. And lots of take-away places have a couple of small tables and chairs or a counter space.
I suggest testing this out on the steps of YOUR local church and see how it goes! What is wrong with people??? Churches are holy places that exist for one purpose: worship.
Dressing like you are running a 1/2 marathon and eating sandwiches and gelato on the church steps is why most Europeans cringe at North Americans. Being an adult in public used to mean something!
I completely agree with the sentiment that it is important to choose your location for a picnic carefully and not offend or impede anyone else.
One of the reasons that I find touring churches in Europe somewhat sad is that many of them are no longer places of worship.