If that were to occur, then it would cease to be council tax and instead just become general taxation, would it not?
Council Tax either needs to stay close to its current form, or effectively abolish it and fund many council services through central government expenditure and taxation.
And once you move away from the current set up, you have to develop new pricing systems - which still have to be related to house prices in some way, but not entirely - as well as mechanisms to maintain incentives for councils to be efficient.
It’s an exceptionally difficult problem to address, which is doubtless why the current system has existed for so long.