Offshore registered properties without named beneficial owners are only a problem if you allow UK freeholds to be held by shady foreign entities and don't have an especially punitive tax regime just for them.
Council tax style systems suffer from property owners (particularly private householders) often not having disposable cashflow remotely comparable to the value of a house they might have acquired many years ago, especially pensioners and especially in London. (whilst I'm sure in practice, private sector equity share schemes wouldn't be too unhappy to lend the house-rich the cash, I can't see council taxes as aggressive as hypothtetical capital gains taxes being politically possible)