This seems to assume a monopoly supplier charging monopoly rents, but is an untenable conclusion if housing is supplied in a competitive market. (It also neglects the fact that its not a flat subsidy, but one where the subsidy rate is positively correlated with income, so that -- within the limits of the deduction -- higher income earners get a higher subsidy rate, and thus the spread in buying power between them and lower-income earners is increased by the existence of the deduction, which even in a monopoly-supply situation would mean that the effect across the market was not "everyone gets the same houses as they would without the subsidy, just at higher prices".)