Jeremy, is that you?
Look OP, if it helps then, despite its name, think of it more as insurance rather than a tax.
People insure their houses and cars so that IF anything happens, the money will be there to put it right. Most people will never have to call on it. So if someone else's house burns down, your premiums will go towards their payout. If the same happened to you, then other people's premiums would be part of the money you get as compensation. What you're 'buying' is the knowledge that if the worst happens, you won't have to finds thousands of pounds to put it right.
So Council Tax - you're paying it so that IF your bins need emptying, they will be. IF you need to use a library it will be there. IF you have children and they go to school, there will be a school for them to go to. IF you need care in your old age there will be public funds to pay for it. Etc...
If you do turn out to need care in your old age, are you going to refuse to take it because tenants will have made a contribution to the cost?
Yes as a PP has explained, most fixed taxes are regressive. Unless you're going to abolish all taxes except PAYE, and increase the % rate accordingly, then there is no way round it. But somehow we have to pay for the things we take for granted. And as for the argument that council tax doesn't pay for these things because it only accounts for 25% of council expenditure, it's nonsense. It pays for 25% of the cost of schools, of lighting, of social care. The rets as you say comes from government, and much of it will have come from general taxation, you know, PAYE which is proportional to income.