When is the last time that cats got into the kitchen cupboards and contaminated everything that wasn't in a sealed glass or plastic container or can?
Never.
When did mice do that? Summer of 1993, when the City decided to save money by not mowing the long grass along the city-owned boulevards and roadsides. In some parts of town (including my area, which was near a wildlife sanctuary and close to the migration corridor), the mouse population exploded because they suddenly had lots more habitat. They became such a problem that year that a neighbor actually begged me to rent her two of my cats, to catch them. I said no, because she had a vicious dog (apparently it never occurred to her that dogs can be mousers, too).
And I rather suspect that rats would be useless at keeping a person warm in the winter. One cat is as good as a spare blanket, and two or more are like a quilt.