Wrong
Under the "fair tax" you have to pay the interest in a lump-sum up front. That's a HUGE "opportunity cost" If we plug into the Future Value (FV) function of Excel we get the following information
For every $100,000 of house value, and assuming a historical mtg interest value of 7%
Under Income Tax, you will have paid roughly $2,300 in taxes on the money you used to pay your mortgage with. And assuming a 30% marginal tax rate, you will get on average $1500 back on taxes for the average interest you will pay.
That means that over the 30 years, you will pay roughly $24,000 total in taxes on the payments you make. Half of that (the average outstanding over 30 years) over 30 years is an "Opportunity Cost of $176,766. So you will have lost $178k in potential earnings due to the cost of paying taxes on your mtg payment over 30 years (assuming a historical ROI from the stock market of 9%)
BUT for the "fair tax" all the tax is paid up front. So the "opportunity cost" is a lot simpler. It is simply how much money your $23,000 could have earned at 9% interest over 30 years. That is $338,803.
So that means that if you buy a new house, for every $100,000 of house value, BECAUSE you PAY UP FRONT the full tax amount, it will cost you $162,032 MORE.
So sure, your "deduction is trumped". But you it costs you $162k/$100k of house value to get that "trumping".
That's a pretty silly and expensive tradeoff.