Renting in general would be a relatively more attractive way to be housed. Most renters wouldn't bother to rent to themselves and would end up sharing the savings with landlords in a competitive market. The housing market would be more rational without the distortion of the tax break.
It would appear that you missed my point. Please allow me to try and discribe in more detail.
Our homeowner currently has a tax break for the interest on the mortgage. We then change the laws so that they no longer get the tax break. The homeowner then responds by creating a holding company and transfers the ownership of the home to the holding company. The holding company then rents the home back to the home owner for the cost of the mortgage, HOA, taxes and insurance.
This then allows the homeowner to have the company take the cost of the house via depreciation, plus the cost of interest, plus the cost of the HOA and insurance as an operational expense under the business. This in effect becomes a deduction.
So instead of just allowing the interest to be a tax deduction, you now have a lot more that can be deducted. The law of unintended consequences and the law of adaptation of the market will cause the revenue to be far short of the anticipated $2 Trillion. It might even create an environment where there is even less revenue because so many of the targeted tax group adopts tax mitigation strategies.