You can't install AC units on the outside of your building in Rome to maintain the architecture, which is the same as saying you can't have any at all.
I recently traveled to Rome and in both places we stayed there were AC units mounted below the windows. We also saw some split systems that had the condenser unit either in a foyer/lobby (hooked up to a vent) or on the roof.
Maybe that's not typical.
Protecting the architecture is understandable, but there are plenty of indoor and portable units.
You can vent AC’s heat out through a chimney. Window units are cheap and reasonably efficient, but not the only option.
You can run an AC inside the building, you just need to exhaust the heat out, which can be done through a window. Do an image search for "portable air conditioner window vent" and you'll see some examples.
I think you're just talking about the historic portion of town?
Of course it's not in every single building. Where I grew up we had AC, but where my grandpa lived for example you couldn't. Just saying that the root comment isn't completely wrong, it happens.
In Switzerland it's just not allowed to install central AC with some exceptions AFAIK. But most people rent, so those window installed units aren't really an option either (can't just drill a huge hole for airflow next to a window). Many offices do that nowadays however, work impediment is just too big otherwise.
Any reasoning behind central AC not being allowed? Just energy efficiency?
Until a couple of years ago it was IMO not necessary, especially for modern buildings with good isolation. Hot summer was maybe 2-3 weeks. But now I wouldn't say that anymore, but Paris agreement / trying to protect the climate as hard as possible is still more important than this. I do think however that we need to take measures to protect the oldest and youngest inhabitants.