Re: That may be true
Mobile phone masts have local backup power that is legally required to last a certain number of hours. I forget the exact spec.
Same as local loop for landlines. Fibre to the cabinet has sometimes required the cabinet to be moved so the batteries fit.
Of course, there's nothing saying that the backup power has to support 4G/5G or Internet DSLAMs, only "voice", whatever that means.
So you're just as likely to lose Internet either way.
In many places mobile is more reliable than landline, because it only takes one tree or flooded duct to take out all landlines on a cabinet, while most urban areas have quite big overlaps.
Also you can take a walk down the street looking for signal. Can't do that with a landline.