The AT&T (BellSouth) remotes around here installed in the last 10 years or so typically have natural gas generators installed, and the COs have a pair of generators for redundancy. Even many of the cell towers have generators. The telco infrastructure is pretty well backed up (I don't know how well tested any of it is of course).
On the other hand, it appears that the cable infrastructure doesn't even all have batteries (I know some people whose cable voice and data services blink with the power).
Yes. In my neck of the woods, there have been a countable number of times in the last few years where when you pick up Vzn POTS, you don't get dial tone. Cellular tends to work well. At least, when combined with Glock, I feel safe enough to rely on it for home safety issue (E911).