It may be difficult to persuade someone that making plans for becoming 'ga-ga' , (as posters have so eloquently put it), is a sensible move. Who wants to think about that as their future?
It can be simpler/less threatening, to think about a future where, whilst recovering from an accident/stroke/major surgery/Covid , one is simply not up to making phonecalls to a bank from one's hospital bed. And so, the builders/garage/council tax people, who want their bills paid,and are not prepared to wait, may simply decide on court action/bailifs.
That would be an expensive pain, and without POA no one could help, as modern regs prevent these people speaking to anyone else.Unless, someone has POA, and can act as your personal assistant, until you can take the reins back yourself.
So, it can be simply a means of allowing a trusted relative to help you out, until and unless you're back on your feet.
This is not a fib, btw: people tend to think of POA as connected soley to an irreversible decline(and it often is). But the mental capacity to deal with your own affairs is not a fixed state: someone unconcious for a week has definitely lost mental capacity, but may later regain it.
It can be easier for elderly people to contemplate a temporary frailty, whilst thinking about an irreversible decline is stil too painful/frightening.