Most people have cordless phones. How do they work in a blackout?
The handsets continue to work just fine, because they have rechargeable batteries in them,
The base stations, however, are a different matter. Most of them do not have rechargeable batteries in them.
The solution is to always have at least one standard phone. If you're sensible, you put phone sockets and a standard phone anywhere you have a handset charging station, because you never know where you'll be in an emergency (like a fire that incidentally happens to burn through the electrics and trip the breaker). Standard phones are cheap enough. You probably have the sockets already from back before you bought the cordless phones.
My view is that the reason you have a cordless phone is so you can wander from room to room as you talk (go to the kitchen for a snack, go back to the computer, have a piss, etc.) and you have an ordinary phone for when you've lost the cordless or in an emergency. YMMV.