This states that mortgage interest deductibility reduces rents basically because it reduces operating costs for landlords. Because it reduces rents then it helps renters, therefore it’s a good idea.

But if it’s good because it helps those on lower incomes, then we need to compare it against other options (government owned housing, rent subsidies, or just plain handing the money to those on lower incomes).

To decide if it’s a good idea, you really need to assess the return on investment compared to other options. Just because it helps doesn’t mean it’s the best way to spend (what I presume is a super massive amount of) money.