By your argument @Bumpitybumper any single childfree/childless person who needs social care has more than paid their share. They've paid for the education and healthcare and other costs of raising other people's children. They're therefore entitled to something back, such as if they need social care.
Also if you want to go down that road, then maybe the childless/childfree wouldn't need local authority funded care if their working life taxes didn't fund other people's kids - because they'd have more savings to use to fund their later life care. It's swings and roundabouts when it comes to everybody contributing to society.
Not many nieces, nephews, cousins are going to devote enough time to become carers in a meaningful sense. Statistics show this.
I can only give anecdotes but my dad helped care for his cousin, and my friend helps her elderly uncle.
Slightly related regarding adult children. Commonly the one who cares for elderly parents is the single childless/childfree adult child, because their siblings are busy supporting their own kids.
Separately, many adult children can't or won't care for their elderly parents. Live too far away or can't afford to give up their job or simply the care needed is too difficult to manage for a non professional carer.