Housing vacancy is essentially a red herring when it comes to the housing crisis. Vacancy rates are still low overall, and reducing vacant housing would barely make a dent in the issue. The real issue is that there isn't enough supply for a given level of demand (i.e. how many people there are who do or would like to live there). Cities have added way more people than they've added housing units over the past several decades.

So would you say the same applies for property which is being underutilized? Throw out the rich people living in 5 bedroom houses? Throw out the grandmas living in the house they once had a family and children in? Mandate minimum number of persons per square foot?

Houses that are vacant for a long period attract higher council tax in London and the whole of England.

Of course you may argue that the difference is small in relation to multi-million pounds properties, but that is a more general issue with the council tax's range.