I faced a similar situation a while back, I have family who are late 70's and early 80's and have grown up regarding fixed line telephony as 'the standard', the properties they live in are either a tiny little hamlet in the middle of nowhere or a rural village that's regularly cut off/looses gas/water/elec. in winter. I made the choice to pay for mobiles for them as a convenience because it made sense. Between medical emergencies and breakdowns on rural roads, I pushed the issue. Initially they were very indifferent, neither really wanted a mobile and in the early days and finding a suitable network required a little bit of trial and error. Now both use them daily, friends either message or call and in a world where unlimited minutes and texts are a thing, it's actually been embraced, the only minor issue was when they decided to donate £50 to charity by text without thinking about who paid the bill

I was expecting a similar resistance when VoIP became a thing, so discussed it ahead of time, only to be told that really they weren't that bothered about the phone lines anymore, mobile coverage on the network each is on covers pretty well and honestly, it just means fewer cold calls. First property dropped landline and went over to fibre last year, next is due some time this year, neither are bothered about losing the landline.
If fixed telephony is absolutely a requirement (red care/alarm/change is completely impossible or similar), move the number to a 3rd party provider for £2/m and buy an adapter for the existing handsets along with a UPS to cover the router, adapter and phone(s). Most OEM UPS batteries seem to do at least 5 years from new, 'equivalent' seem to do less, but even if you regard it as a total loss rather than replace the battery, you're still saving hundreds of pounds going this route. Of course there will be extreme fringe examples, but people living in those situations generally have a generator, food, water and everything else they need to survive a few weeks anyway because they know that's a thing - if the mast UPS or the PSTN phone supply goes down, it doesn't matter what you do anyway.