If I was in charge.
I wouldn't change the whole council tax system, it broadly seems to work, it's well understood etc.
the only change I'd make would be to stop council tax relief on empty properties.
I think this would be a "stimulous" to cut rents and get properties occupied.
it would also make buy to leave housing much less attractive.
I'd close some loopholes - where they exist without good reason, (e.g. it'd be difficult to close the VAT loop holes for businesses based in Jersey (where Amazon used to have a warehouse) are difficult to close, they are there for a reason (to help flower farmers) but are abused by multinationals (e.g. Amazon) to avoid paying VAT.
I'd change the law on tax evasion, making companies liable to pay their tax bills in the country where said sales are made, not where companies are head quartered, and making CEO and CFO staff personally liable to be charged and imprisoned, (staff at this level should know what is happening in their company. - weird and wacky tax avoiding schemes will have passed under their nose.)
I'd improve the systems used in paying benefits, this would tackle the 1bn over payment problem, (which either looses money or traps people with repayments that they can't manage!) and would help prevent fraud.
I'd make it more financially rewarding to "shop" people who don't declare all their earnings. or who genuinely "cheat" the benefits system, (like the cases with the woman claiming to be wheelchair found water skiing in florida etc.) or at the softer end of the scale start a campaign to show what taxes are actually used to pay and provide for, and attempt to change social attitudes towards defrauding the system.
none of those things are cuts. but would represent a massive reduction in costs to the state.
but in answer to your original question, no, I don't think that blindly and bluntly cutting anything will be "good" for anything,