agreed, the people that haven't got private pension tend to fall into 2 categories, 1) spent their whole life earning low wages and couldn't put anything away. There are huge numbers in this because the state effectively sponsors this kind of worker exploitation by having a very low minimum wage. They've made an imminent crisis by doubling down on this and having things like zero hours contracts, and subsidising low wages through our benefits system. Another 30 years, state pension issues are going to be much worse as many, many more people will retire with nothing. 2) Keeping up with the jones's attitude of spend it and prove how rich you are rather than save for your pension, people living beyond their means, and would rather have 2 holidays in spain every year than save.
I'd argue that we are getting more and more people in that first category, and I think it will reach crisis level one day.