The cost of moving including fees and taxes is astronomical and would pay for years hof higher council tax.
Also, bands need to be reassesd. There are low band properties where I live which are much larger and more luxurious than some higher band properties, so it seems quite unjust.
Another huge issue is that this is levied differently across the country. A literal mansion in Kensington pays less council tax than I do on my (nice but not luxurious 4 bed) in a rural area. We pay loads but have very little services, and could not afford to move to Kensington even if we wanted to.
I have no issue with paying tax, and am happy to do so in a progressive redistrabutive system. We have paid a lot of tax over the years. However, in my view Council Tax is neither fair nor efficient as it stands. A well implemented Land Value Tax might be a better solution, and be a more equitous approach nationally than the current system we have.
Also, as other posters have pointed out, Council Tax is devolved, so new rules only apply to England. Wales rebased the bands in 2003, and a new law states that the system will change as of 2028 when properties are next valued for CouncilTax. From then on they will be revalued every five years. This should at least stop people being punished for house price inflation/timing of purchase and getting soaked for decades for higher Council Tax than the mansion next door. England could choose to do this if it wanted to - the data is much more easily and cheaply collected now since so much of the sold house price data is online.