The UK Government are offering a pension topup scheme details here:
Going on the above example, it would take 20 years to recover your initial 4k outlay compared to just putting that money in the bank with a 1% savings rate (which you can easily exceed if you're savvy).
By that point the guy is now 88. Even if he lives another 5 years he's still only £1400 quid up. And thats an ENORMOUS IF.
PLUS what on earth will he do with an extra 260 quid a year when he's 88. Nothing useful. It wont cover the no doubt enormous costs of care, so it just doesn't make any sense to me whatsoever.
There is one option - perhaps he hates his children and wants to ensure they don't get as much inheritance?
Perhaps there is a use case, some combination of age/gender etc, personal circumstances, where this does make sense?
(The government does already separately offer schemes for women who dont have enough NICs to top up their pension - so it's can't be that example)