Yes, the banding system and also huge discrepancies by area really need sorting out. The whole thing needs a huge overhaul really, to make it fair.
PPs talk of downsizing if you're single - well where I live, pretty much everything is band A. It's not posssible to downsize and pay less! Plus however you look at it, a couple will pay less per person even in a one-bed flat. Bearing in mind a single person is also having to pay much more in rent and so on, it IS unfair.
As for encouraging people to have children. Great. Society collectively contributes towards the next generation. But doesn't explain why a childless couple (or with adult children) should pay less per head than a single person. Also anyone who thinks it's a "lifestyle choice" to be single, or even in many cases to not have children, needs to give their head a wobble and have some empathy for those who would have a loved a family but didn't get the chance. As for saying "get a lodger or live in an HMO", perhaps they should actually stop and think about whether they'd be happy in a house shared with strangers, or who they know that they'd be happy to live with if they were single.
Also the talk of how much of council tax goes on social care matters just as much when considering couples/larger households, as when considering single people. Again, if we're collectively funding social care, why should those in couples pay less per adult?
People always talk of poll tax in these discussions, and how it wasn't fair that each adult in a multi generational household had to pay the same rate as the lord of the manor paid. (Not more - the same per adult.) So your family with say four adults kicks up a fuss. But they don't consider the family next door with only two adults and three DC to look after, or the regretfully childless and single lady in the tiniest property at the end of the street, who's already in poverty just by having to pay the rent alone. It is not fair that these people should pay more per adult.
I get the broad idea that people with more should pay more, but single people generally don't have more, precisely because they're already shelling out on everything else alone. If the property bandings were sorted out and actually fair/logical, the lower bandings at least should have a single person discount of 50%. Because they are already in a small property, not wealthy singletons in large houses. Although two wealthy people coupled up in a large house should really pay more than one wealthy person anyhow!
There's so much wrong with council tax that personally I'd scrap it and increase income tax to make up the difference.