But the difference with that is that you benefit from more adults working. If you are a pensioner now, if those adults weren't working, where would your pension come from?
I don't even have children, yet I can see the wholesale benefit to the nation of every child receiving some level of education. You chose to send your children to private school. If you had found yourself unable to do that, the state safety net was there. Your children wouldn't have been without any sort of education. You paid for a safety net. Just like I pay for those on benefits in the knowledge that that safety net will be there for me if I am ever unfortunate enough to need it.
Pension payments are no longer that safety net. OK, it's never been an absolute guarantee, but now it's no guarantee at all.
The 30 something pp doesn't have a choice about whether to contribute to a private pension fund of some sort. She doesn't have the safety net of a state pension. She'll likely be solely reliant on what she has paid in to her own pension through work etc. Yet she, like you and me, will also have paid into it.
It won't be that she can say, 'well, luckily I have never needed it's, it may not be there even if she did. It's a safety net she doesn't have.