I feel like comparing house type would be more useful really.
E.g. I live in a 2 up 2 down terrace. It's value will vary from well into the hundred of thousands to a couple of hundred grand to maybe £75k, depending on the area.
But it will still be the same house no matter how much it costs.
In my area it's a band A and that is about £1500 without a discount.
I do think social care should be funded centrally by the government though: if councils want to provide slightly different arrangements for bin collection or street lighting that's up to them and I don't mind council tax varying to deal with that. But social care should be consistently provided across the country and so should be funded by national taxation.