That's why you also have to tax away all capital gains associated with land (not structures) value appreciation beyond the real inflation rate. Land (outside of reclamation edge case) is not created by humans, and when land becomes private property it is necessarily depriving the public of the use of that land, thus the land owner owes the public for the right to deprive them of the land in the form of land tax, and since the land owner did not create the land, they are not entitled to any appreciation in the value of the land, that belongs to the public. The land owner is entitled to the returns of their productive investment, i.e. building structures etc. Land price then is largely set by what sort of productive return it can generate, not by the supply of credit and lending standards and supply of greater fools.

If capital gains were taxed away, that would counteract the situation where mortgage tax breaks feed directly into increased prices.

What I suggest above will be very very unattractive to many people, as real estate speculation represents one of the best 'money for nothing' speculations most people can engage in, but speculation is by definition unproductive, and it would seem to be a good idea, if unpopular to engineer a system that discourages real estate bubbles.