It's an issue of convention, which is underneath an issue of power - i.e. who decides the convention? Do foreigners have a right to effectively modify how a place is called? Or does that power rely exclusively on the locals?

For a long time, "foreigners" avowed that right to them: it was the colonial era, after all, and colonial powers were "obviously" right in privileging their rules.

In the post-colonial world, things have changed. It has now been accepted, roughly, that the right to self-determination extends to determining how others should call them and their countries. These rights are pretty new, in the overall history of mankind, and somewhat nebulous, so old conventions linger; but the countries more determined to be treated as equal on the world stage (China, India...) have already put it into action and insisted that their preferred names be used. Not doing so would be uncourteous, a bit of a slap in the face.

Personally, I'm all for the new rule, I just wish it was consistent for everyone. My home country doesn't contain any "Florence", but it does have Firenze; the above-mentioned Padua is actually Padova; Venice should be Venezia, Rome Roma, Turin Torino, Genoa Genova, etc etc.