How would a renter feel if their rent increased because their landlord was unable to take a mortgage deduction? In other words, is the deduction implicitly distributed pro-rata to the supporting renters via market force?
In the US, the home mortgage interest deduction does not apply to rental properties. To qualify for the deduction, you either have to use the home as your residence for a minimum period each year, or rent only part of it (and meet requirements for renting part of the home: you can't have more than two tenants, and the part of the home they live in can't have its own separate kitchen or toilet facilities).
But that's the home deduction. Apartment buildings, for example, are investment property for which mortgage interest is a deductible expense. https://www.irs.gov/publications/p527/ch01.html
Then you concede that taking away the home mortgage interest deduction (making the homeowner-who-resides-in-the-owned-home and the renter equal for tax purposes) would not drive up rents, and your original comment was at worst wrong and at best a non sequitur.