I think there needs to be thought into where the money is going and not just where it's coming from.
Care home fees cover the basic costs of living - a roof over your head, food, gas, electric, cleaning, maintenance, bedding, towel, TV licence, gardening, security and then for care and maintenance of things that are needed to care - staff (and the costs they incur like DBS, tax and NI, training, uniforms, PPE as well as wages*) equipment like hoists, stand aids, slide sheets and profiling beds and the extra electricity to run the ones that rely on it, maintenance of them, replacement, replacing items broken and ruined by residents due to their needs or behaviour like chairs, tables etc.
*I'll just say that not all but many companies expect staff to buy their own DBS, uniform and don't pay for training, some I have heard charge staff for training (though that's never happened anywhere I've worked).
In theory, the more you pay, the better care you should get because there should be more staff, better trained and paid, more equipment that's better, better food etc. But every home has to meet the needs of their residents, maybe room 3 doesn't need a hoist now, so why are they paying towards it? But what if they fall and need it for a few weeks - should they then pay more? Or should the home use the hoist they already have anyway and should they have these things regardless because a high proportion of residents will need one at some point?
What I'm saying is that does all the money that's being paid by self funders and LAs go towards care and there's a shortfall so the costs aren't being met? Or are we funding bargain style care to maintain company profits?
I know one thing, the workers delivering the care aren't getting a very good deal either, especially when they're paying for the essentials to do the job themselves out of minimum wage and the residents aren't getting much of a good deal if they're paying more than the LA will but recieving the same care.
Ultimately though, funding everyone for free social is going to cost a lot more in the way of tax than we pay now, which will be ok for the higher earners, not so great for people like me who can barely survive on what I earn now never mind with more taken off.
I don't know what the fairest answer is, but I don't think any model of funding will ever be truly fair for everyone.