Housing is less expensive, but housing costs aren't high because of the tax paid on them.
Not true. In Germany, approx. 80% of the population rent - they don't own homes. Because of this, there's a generally big interest in keeping rental prices steady... because 80% is one hell of a majority vote, and legislation is designed to benefit tenants, with all laws heavily falling in their favour. In addition, rental cost must adhere to the Mietspiegel - and index that tracks the rental cost in any city or state. People either rent from big consortiums or private landlords. There's healthy competition. Because many people prefer to rent, rather than buy, property prices don't go up in the same manner as here in the UK. Landlords generally buy property for the income it produces, not the growth of the property value - which is what it should be.
Also, one major thing in keeping house prices low is very prudent bank lending. LTV ratios barely ever go beyond 80%. In fact, a 20% deposit is often seen as no enough, when here in the UK, it is seen as "too much for us to save".
If you look at UK house prices, they have only really started growing exponentially when in the 70s, the law was changed, allowing high street banks to offer mortgages, and not just building societies. Competitions amongst these financial institutions increased, resulting in mortgages being made available to a wider population. Within that decade alone, house prices increased tenfold, because prudent lending went out of the window...
House prices really don't have much to do with tax, but rather supply and demand. Suppy is limited because the UK is a very small country, that does not really "build into the sky". Demand depends on how many people manage to get hold of the money...