That is one of the issues with the alternative phone services...the loss of service when you lose power. The traditional phone service is powered from the central office and they normally have long term power back up (assuming you have a direct connection to the central office). In the event of power failure you still have a dial tone as long as the wire between you and the central office is intact. The small UPS provided by the cable company, or by the phone company where you have fiber to the home is not near as reliable as the old POTS phones.
Indeed. Even if you have reliable emergency power you're also at the mercy of any active equipment along the line.
As you said, only one point of failure for traditional phone lines: The giant battery banks at the central office. It gets a bit more complicated with RLU/concentrators but they usually have similar coverage (around here they'll run for about 24 hours then they'll send out guys with generators, about a dozen sites)
Cable TV & Phone can have two or more points of failure: The headend, the fiber>coax node, and one or more amplifiers along the way. Generally you're at the mercy of the batteries in the pole-mounted power supplies which run everything outside the headend. Typical runtime here is about 4 hours on battery. Once they're gone you're SOL. Way too many units for them to run around with generators.
Our Telco is transitioning to GPON fiber. It's a bit better since there are no active components between you and the central office. Same big batteries at the CO, and if you've got backup power you're laughing, regardless of the puny battery that comes with the ONT
