I'm not arguing for a life insurance scheme, but am saying that whenever someone mentions the amount they have paid in they are 'trumped' by someone else pointing out that there is no 'pot', as though that negates the fact that most of us pay a significant amount for decades. IMO that is not the point being made, which is that nobody is told that they have to pay 13.5% (or whatever it is now) of their income to those currently claiming a pension, and it will simply be the luck of the draw as to whether they will get one themselves when the time comes. The implicit deal is that you pay in and you get out. Yes, some choose not to pay in, and others are unable to, but they are separate issues.
I think pensions should die with us, so that, as you say, those who are lucky enough to claim for years because of longevity can do so. It's unfortunate that some don't even live to pension age and others die not long afterwards, so don't claim for long, but there is no other obvious way to do it.
If there is no compulsory scheme such as NI, we would end up with people who had no means of support in old age, and the choice would then be to let them die or take the money from somewhere, which would be Hobson's choice.
Maybe it would be better to have individual pots, but that would bring its own problems, such as the cost of administration, the lack of cover for those unable to contribute, and the problem of what to do with those who don't work and make contributions if they end up destitute. Currently their pensions are paid for by those who do pay in, but individual pots would mean that wouldn't happen.