"We live in Rome."
I suppose that your sentence is technically also correct if your exercise is to translate the English "we live in Rome" to Latin. However, Romae vivimus more accurately translates to the English phrase "we are alive in Rome."
In my experience (native US English speaker), "to live (somewhere)" almost always refers to a place/location where a person's home is found. Only in very, very rare and specific contexts would I ever interpret such a pharse to mean someone "surviving" (or simply "being not dead") in a specific place/location.
It is for these reasons that I would argue that your suggestion of Romae vivimus could mean "we live in Rome" in the most literal sense but it does not capture the much more common meaning that is represented by Romae habitamus and so I do not think that both should be accepted here. In my opinion, only Romae habitamus conveys the intended meaning in both English and Latin.