People who work for the council do pay Council Tax, unless they qualify for an exemption, just the same as everyone else.
Just the same as members of the government pay taxes.
This doesn't mean they can't be criticised for wasting 'public' money.
It's like putting someone in charge of a holiday club, and instead of them carefully looking after the other people's money, and sharing it out when the holiday starts, they decide to spend it all on stupid designer sun hats for everyone.
If you don't want a daft hat, and would rather eat ice cream, and ride a donkey all day, you'd have every right to complain.
