While rats are blamed for the Black Plague, it was fleas that transmitted the pestilence to humans.....
I can't imagine any scenario that makes rats a plus, perhaps long term confinement, or starvation.....
While a managed pet rat may pose little threat, rats in the raw have no toilet decorum, current health threats associated with rat feces consist of hantavirus, (common)
Also the aforementioned black plague (very rarely due to its lethality),
Rat urine is responsible for the spread of leptospirosis,
Lymphocytic choriomeningitis (LCMV), a viral infectious disease, is transmitted through the saliva and urine of rats.
Multiple secondary infections come with parasites that feed off rats.
Beyond the fleas that afflict poor Fluffy, a twice a year deworming is appropriate for any creature dining on wild rodent.
Rats will chew through drywall, pine, (or any softwood).
Rats will bite if cornered.
For rats in entertainment.....Read (or listen to) Gil Scott Heron's "Whitey on the Moon"!
https://www.youtube.com/watch?v=goh2x_G0ct4