I would actually argue for an opposing viewpoint. Rather than eliminate the mortgage interest tax deduction, allow the interest on
all debts, and rents, to be deductible. If you really need to tax that money twice, raise the tax rate on incomes earned from interest and rent.
The problem, as I see it, is FNMA and FDMC. Those entities, whose purpose was to ensure that a market for residential mortgages would exist, is now actually just engines for inflating housing prices and commoditizing low-risk real estate investment. They are the means by which an investor may become an absentee landlord without assuming any of the normal responsibilities of property management. Ordinary people volunteer to maintain and improve the investment properties, because they are offered the illusion of ownership.
A wise and shrewd financial plan can certainly make the mortgage system work in one's favor, to produce genuine ownership, but for the most part, it has done little more than create another class of resident somewhere between owner and renter: the mortgage-payer.
Having been both renter and mortgage-payer, and having seen some of the ugly hidden details of the US housing market, I do not recommend that anyone in the US software industry actually choose live in a mortgaged home except in the following places: New York City, Chicago, Washington DC, Austin, Seattle, Boston, Portland, Phoenix, Denver. (California properties near LA and SF are simply too overvalued, in my opinion.) Nowhere else has a sufficiently dense industry to ensure that one can work an entire career in the same place without sacrificing higher regular pay as an alternative to moving.
I would still like to actually own my own home one day, but as parent poster mentioned, I have done the math, and determined that I would be better off renting and saving, rather than borrowing and paying. And one of the major reasons why is that I have little sense of certainty with respect to where I will be living in five years, and that is roughly the absolute minimum timespan required before taking a mortgage can become less expensive for me than renting. Another is that any event likely to force me to move to find work is also likely to depress local property values. I would prefer to park my net worth in an asset that rises in value when people like me lose their jobs, and in assets that I am not forced to sell when I move, lest they become a financial burden. The money I save can be used to buy a retirement home, after I am done worrying about the consequences of place involved in moving around or staying put.
The problem with that mass-market forced-savings program is that dumping all your retirement funds into just one depreciating asset is just a horrible way to retain value. The only reason it works at all is because it forces people to literally sit on their nest egg. They must be aware and cognizant of everything happening to it, and actively defend against any threats to it. It forces people to be active investors in a market they are familiar with, because they live in their own neighborhoods.