The concept of imputed income also helps homeowners. If you own a house that you rent out to people, the money you get is counted as income. If you are an owner-occupier and paid off your mortgage, then you effectively pay rent to yourself... money that you otherwise would've needed to pay to others, but don't need to pay tax on it.
So essentially you get a deduction even besides the mortgage interest deduction. All of this is also factored into home values, and thus the purchase decision for new buyers won't ever be dramatically better than renting.
The solution of a land value tax is necessary. It is most necessary in the residential space, including for first homes, because that is the most important place where we need to ensure high and quality supply, and affordability.
Helping homeowners, specifically, but not others is arbitrary and unfair.
Providing a citizen's dividend out of the revenue of a land value tax, to help all, would be fair, and would help enable people to acquire homes if they want them.