Rental properties are convertible to condos. If you make money available to buy property then exactly that happens, which reduces the supply of rental properties available to the people who can't afford to buy even with the mortgage subsidies, thereby increasing rents.

> It would tend to drive down rents by: lower returns in other passive investments might drive investment towards rental real estate chasing income (increasing supply), steadily increasing property values might encourage marginal buyers to buy, reducing demand on rental units in an area, foreign buyers might be more inclined to "park money" in USD real estate, some of which could be rented to offset the cash flow.

Rents are directly related to property values. If property values are higher it takes more capital to purchase a property in order to rent it out, which requires higher rents to justify someone doing that instead of allowing the property to be sold to a resident.

In theory mortgage interest subsidies might not increase property values if the market responded to the demand by increasing the housing supply. But then zoning laws prevent that from happening, so they do.

And there is no reason for someone who buys housing for speculation to rent it out at below market rates. Moreover, it has been a major problem that many of those people don't rent it out at all because at scale not renting it increases housing prices (which is what they want as speculators), leading to a large amount of unoccupied housing in the midst of a supply shortage.