We are going to Venice, Florence and Rome in late September and packing only carry-ons. I plan on taking 3 pairs of shoes. Is it really necessary that one pair be closed toe? If so, is it because of the weather?
I think this is a personal choice issue! Yes it may rain in September so closed toe shoes might be useful to have along. Tromping over ruins and cobbled streets really calls for sneakers or walking shoes (for comfort and safety). But exercise sandals (like Ecco for example) work well. Keens do a good sandal exercise sandal that does have closed toes. I am off to Crete (small town, beach, hiking ruins) and Rome (ruins, galleries, walking, walking, more ruins) at the end of August and am taking sneakers (wearing on plane) and one pair of Eccos and one pair of flat sandals with bling.
Nobody will require them unless you go somewhere pretty fancy. On the other hand after you have seen how filthy your feet will get in Rome, especially, and Florence you may wish you had them. Rome is paved almost exclusively in medium to large cobblestones with big gaps between. Those gaps and the surfaces of the cobblestones have the dirt, detritus, and filth of centuries and soon feet in open footwear have too. Also, because your feet will be walking on these not-very-level cobblestones I find that ankle support is critical. For both reasons I wear supporting hiking boots everywhere in Rome. I find that in Florence the baking heat and omnipresent dust make walking in casual footwear difficult. Also, the pavements (sidewalks) are often very narrow and my feet like support going up and down kerbs (curbs). Venice is pretty clean under foot and uses quite large paving stones. Its only a question of if the bridges would cause you any problems. I often wear Crocs in Venice when the hiking boots want a rest.... Then again, YMMV
I wore sandals most of my trip in Rome and Italy...mind you, on the few rainy days we had, closed toe were a must... (I packed my beloved Blundstone boots - great at the airport - easy on/off, waterproof and soooo comfy...but 2nd trip, didn't take sandals and my feet almost died from being so hot)...as well as other places that involved rough ground - like Mt Vesuvius/Herculaneum and some hiking trails in CT. And the nights do cool off. That being said, the sandals I had were very comfy (Naot) but had a little higher sole - about maybe 1.5-2 inch wedge - I never inspected my feet, but I didn't find that they were dirty at all...but I don't think I'd want to wear flip flops or very thin soled sandals.
My wife and I wore open toe sandals through Venice, Florence, and Rome (and others) with no problems. The only place that would've been a concern at all was Rome, as the cobblestones can be slightly treacherous, but it wasn't much of a problem. A friend also recommended closed toe shoes to us, and we had a pair with us, but stuck with our sandals anyways. I think the only reasons you may want closed toe shoes is if you'd prefer them in the rain, you're worried about your feet getting dirty, or if you are clumsy. Otherwise, I wouldn't bother.
'you're worried about your feet getting dirty' That and the knowledge that some people think they get their clothes clean in a sink can make you real damn picky about with whom you travel.