Its pretty common in the US. There are a lot of availability requirements on residential telephone service, so if the customer in the US bundles in phone service their device usually comes with a small UPS. Verizon ONTs usually had a battery backup built-in to the wall unit. AT&T's gateways had a UPS as a part of the 12V adapter. It seems like maybe these rules have relaxed a bit, but its still relatively common to have your home internet connection and phone service on some level of backup.

This goes back to the idea that POTS usually had its own power service, so when the power goes out the phones would often still be working. When things changed over to fiber and VoIP, similar availability requirements were being applied. As mentioned I'm not sure if this is still the case, I haven't bundled phone service with internet in well over a decade.

Ultimately though of course I would put at least core network things on a UPS (ONT, router, PoE switch for APs) as if the power goes out I'd want to be able to see WTF is going on. If its a big enough event to knock the power out for a little while there's a decent chance it could also lead to lots of people stressing cell networks, so you might not want to rely on that. For those core things I have on a UPS, a small-ish gel cell battery would operate them for a bit under 4 hours. I live in an area prone to both tornadoes and remnants of hurricanes though, so I'm in semi-disaster-prone area.