It's not as regressive if you charge sales tax on housing.
In point of fact, the US mortgage interest deduction is highly regressive. It favors those who can afford a down payment on a house over those who can't, who by definition will be poorer.
If the sales tax applied to buying a house, it would be quite progressive. It could even only apply to the cost of the house less some amount (say, $100k) which would make it even more progressive.
Property tax already does this, right? China has a sales tax on housing but no property tax, which seems to exacerbate wealth inequality there as people can speculate on property without penalty for not putting it to use.
In point of fact, the US mortgage interest deduction is highly regressive. It favors those who can afford a down payment on a house over those who can't, who by definition will be poorer.
If the sales tax applied to buying a house, it would be quite progressive. It could even only apply to the cost of the house less some amount (say, $100k) which would make it even more progressive.