You’re not paying into a pension pot from which you will later withdraw.
Your current contributions are paying the pensions of those people currently in receipt of the SP. And when it comes time for you to draw your SP, that cash will come from workers paying their NI (some of whom will, similarly, then be contributing beyond the required 35 years).
You've got closer than anyone else on this thread but not quite there.
This is a cycling forum. We're all aware (or should be) that road tax / VED or whatever doesn't pay for roads. It's just another tax.
Roads are paid for out of taxes raised by the government, which includes, for example, VED, fuel taxes, VAT, income tax, capital gains tax and national insurance contributions.
The state pension is paid for out of taxes raised by the government, which includes, for example, VED, fuel taxes, VAT, income tax, capital gains tax and national insurance contributions.
NI is just another tax. Arguably very unfair as it is levied on earned, not unearned income and the marginal rates are greater for lower paid workers.
NI contribution records are simply a method of calculating entitlement to certain 'contributory benefits', of which the state pension is only one, though since 2010 the value of the others has declined significantly or disappeared altogether.