Thomas Piketty in an interview for a British think tank suggests property taxes should be assessed based on your equity in a property (value less debt) not on value:
But it is perfectly possible at the national level to transform our traditional forms of property taxation, which are typically proportional and which do not take into account financial assets and financial liabilities, because they were set up in the nineteenth century when most property was real estate property, so they do not take into account financial wealth and liabilities. This can be turned into a progressive tax on net wealth, which basically would be a way to reduce property tax –council tax in the UK – for the vast majority of the population. Typically, if you have a house that is worth £500,000, but you have a mortgage of £490,000, you are not rich – you have a net wealth of £10,000, so you should pay less than someone who has no mortgage or who paid off his or her mortgage many years ago.
This makes little sense for US property taxes on owner occupied housing as I will explain. Piketty is correct that someone with a mortgage on their house is less well off than someone who owns their house free and clear. However this is already taken into account in the US tax code through the mortgage interest deduction in the federal income tax code. Although this deduction is often cited as a loophole it has always made sense to me. But I don't think it makes sense to provide a second reduction in your taxes for having a mortgage. In fairness to Piketty many countries don't have a mortgage interest deduction in their income tax code in which case his equity argument above has more force. But in those cases a simpler fix is to add a mortgage interest deduction.
I had previously though the real loophole regarding taxes and owner occupied housing was that the imputed rent on an owner occupied house is not included in income. But while thinking about this it occurred to me that property tax is roughly equivalent to an income tax on imputed rent. (This idea is not original to me but I had not encountered it before.) So besides the practical problems in trying to assess and tax imputed rent as income there is a theoretical case for excluding it as well. Of course if property taxes are a surrogate for income tax on imputed rental income they should ignore mortgage debt as this doesn't affect the imputed rental income you are receiving by living in your house.
A complication in thinking about tax breaks on owner occupied housing is that any benefits tend to be reflected in selling prices and hence make less difference to new buyers than might be expected.