You are so correct; that's one of the things I loved about the old white ONT box with the large 12 volt battery. If the power went off, the battery backup turned on regarding my continuing to have phone service.
The the new ONT box they installed over the weekend, if I purchased the battery voice backup battery, it will need 12 D alkaline batteries, and when the power goes out, you have to turn the switch on and when the power is restored in your neighborhood, you have to turn the back up battery switch off. I've decided not to purchase an empty box for $39.99 that doesn't come with batteries. Verizon is getting over on consumers. Verizon should off free back up batteries to it's consumers, senior citizens, and especially if they have a heart problem or some other serious type of illness living alone.
The importance of a BBU has diminished in recent history. The source only buoys telephone service during a power failure while seemingly few FiOS subscribers opt to have a POTS line.
AT&T installs (or has installed) an Alcatel-Lucent/Nokia ONT for their fiber to premises service. The offered BBU functions the same way that the Verizon 211's does.
On the other hand, a good UPS will support full functionality either long enough to casually shut down computers or for extended periods of time. 🙂