The right tax is almost always a wealth tax. Especially for a service that’s for the elderly. They’ll never tax wealth.
How would you implement it? The rich put that wealth in lots of different places and would argue that a lot of it isn't liquid so taxes on it would cause them cashflow issues (whether true or not).
We've got a diverse range of taxes to try and tax wealth via various sources (Income, sales, CGT, dividend, interest, inheritance, import etc) so whether they save it, spend it or whatever it's fair share goes towards helping society overall but they rely on money moving around in some form or another. If they just sit on it it can't be touched. So how do you measure that wealth that is being sat on?
How would you tax someone who owned a Da Vinci for example? Would it be taxed on the value it was bought at? Would it have to be revalued periodically?
What if Banksy did a piece on the wall of your property?
How would you keep track of everything everyone owned and what they were worth? Rely on everyone telling the truth?
Would you force the sale of things like property/land/shares/art if they could not pay the wealth tax on the value of those assets? IMO that'd be more likely to affect the middle class and you'd end up with a lot more property and land ending up in the hands of the wealthy who would likely be more cash rich and able to pay.
If you set a tax whereby a percentage of the balance in a bank account is taken each year then people will just stop keeping money in them. You'd probably have to work it out on a daily basis or people would just move the money/take it out on the day the tax is calculated then put it all back in the day after.
Even if you figure all that out and manage to implement it how do you stop people hiding their wealth offshore or in trusts/charities?
Although not a solution perhaps one thing that could be of use is to add in a sliding scale like we have for income tax into sales tax, so the rich who are likely buying more expensive items pay a larger amount (property would need consideration or possibly exemption). So for example items up to £100 = 10%, £1000 = 20%, £10k = 30%, £100k = 40%, £1m+ = 50%. But even that wouldn't tap into much of the wealth and the truly wealthy could source the most expensive items abroad to avoid the tax in exchange for import tax, unless you did the same with that.
Wealth tax would be the best way but I don't see how to make it work without the rich finding some way to avoid it. Hence why it's never been implemented.