Good points Sofia so maybe it should be a Tax, maybe called the Social Care Levy and paid on a similar scale to Income Tax. Like Council Tax Bills, it could show as a specific Tax in Deductions or Annual Tax Calculations.
There's always winners and losers in any system - eg, Covid Payments, those that chose to limit their Tax liabilities by being paid their earnings via Dividends were losers.
The current elderly population are generally winners, but without wanting to sound crass, they are a 'dying breed'.
And as for the current working age population it seems that 'longetivity' has peaked and we're starting to die younger which, given the stresses of modern life, is hardly surprising. And very harsh of me to point this out, but Covid decimated the numbers of aged elderly requiring care didn't it?
So, we just have to suck it up I'm afraid, we get to pay now, work longer and die younger. In a nutshell, no good moaning about it.