"the largest effect of the mortgage deduction is on household financial decisions, inducing them to increase indebtedness"

From the NBER access page for Do People Respond to the Mortage Interest Deduction? Quasi-Experimental Evidence from Denmark by Jonathan Gruber, Amalie Jensen, and Henrik Kleven:

Using linked housing and tax records from Denmark combined with a major reform of the mortgage interest deduction in the late 1980s, we carry out the first comprehensive long-term study of how tax subsidies affect housing decisions. The reform introduced a large and sharp reduction in the mortgage deduction for top-rate taxpayers, while reducing it much less or not at all for lower-rate taxpayers. We present three main findings. First, the mortgage deduction has a precisely estimated zero effect on homeownership. This holds even in the very long run. Second, the mortgage deduction has a sizeable impact on housing demand at the intensive margin, inducing homeowners to buy larger and more expensive houses. Third, the largest effect of the mortgage deduction is on household financial decisions, inducing them to increase indebtedness. These findings suggest that the mortgage interest deduction distorts the behavior of homeowners at the intensive margin, but is ineffective at promoting homeownership at the extensive margin and any externalities that may be associated with it.

(emphasis added)

The mortgage interest deduction encourages the growth of debt. We could have instead a policy that offers a tax benefit for making an extra payment or two during the tax year. Such a policy would discourage the growth of debt. And it could be designed to offer approximately the same tax benefit as the existing policy.