A couple of years back, was in Rome while visiting my daughter. Used an NEX-6 with 16-50. APS-C so 24-75 in ff terms. I just skimmed over some of my on-line albums to refresh my memory. I don't recall any major problems in "streets" with lens not wide enough/streets too narrow. Except maybe the Trevi Fountain. There's not a lot of room in front of it and usually crowded. Just checked it on Google and the current satellite view was taken while under restoration. Different, drained, scaffolding, much of the building covered up, etc.
OTOH, I found I would have liked something wider quite often in interiors of some of the churches we visited, even St. Peter's and the Vatican Museum.
Also, interiors may not be very well lit so a faster lens might be a consideration, too.