Definitely doing council tax by property value is unfair.
It harms people on low incomes from areas where housing has been allowed, by successive government policies, to become too expensive.
NB. Council tax benefit was scrapped some years ago. Now individual councils decide how much to discount for people on the lowest incomes. Some still give a full discount, others don't.
So today there's a situation where a single income low waged or disabled person on benefits renting a crappy 1 bedroom flat somewhere like London or parts of the SE, could be in a higher band than a dual income owner occupier household with a house from an area with lower house prices.
London for example has the highest house prices in the UK - but the lowest wages (also I know from friends in London that public services are in many London councils pretty much non existent).
https://www.timeout.com/london/news/the-five-lowest-paid-areas-in-the-uk-are-all-in-london-022424
And obviously loads of people from London and the SE can't all just move somewhere else. As well as many especially the vulnerable needing to stay near family or work or support, if loads of people moved somewhere else then that adds pressure on housing, jobs, and public services where they move to.
Better would be increased income tax - used to nationally fund essential services (that also ends the postcode lottery of public service access and quality). And maybe a local income tax done by councils, based on income (and assets, not including the home someone lives in) for nice to have but not essential local services.