No. This logic is dangerous.
The apples to apples comparison between renting and buying should be between similar living arrangements. One can't (legitimately) compare living in a 600 sq ft studio to a 3500 sq ft house.
With the proposal you offer, one should get the largest mortgage they qualify for, but that can result in a house far too big for their needs. Borrowing to buy just what you need makes sense. Borrowing to buy a house with rooms you may never visit, not a great idea.
By the way, do the numbers. The 30 year rate is 4%. You'd need a $250,000 mortgage to get $10,000 in interest the first year, that's a $312,000 house given an 80% loan. On a median income, do you think it makes sense to buy a house twice the US median?
Last, a portion of the tax savings is 'lost' to the fact that you have a standard deduction of nearly $6,000 in 2012. So that huge mortgage gets you an extra $4000 in write-off, and $600 back in taxes.
Don't ever let the Tax Tail wag the Investing Dog, or in this case the House Dog.
Edit - the investment return on real estate is a hot topic. I think it's fair to say that long term one must include the rental value of the house in calculating returns. In the case of buying of way-too-big house, you are not getting the return, it's the same as renting a four bedroom, but leaving three empty.
If I can go on a bit - I own a rental, it's worth $200K and after condo fee and property tax, I get $10K/yr. A 5% return, plus whatever appreciation. Now, if I lived there, I'd correctly claim that part of my return is the rental value, the rent I don't pay elsewhere, so the return to me is the potential growth as well as saved rent. But if the condo rents for $1200, and I'd otherwise live in a $600 apartment with less space, the return to me is lost. In my personal case, in fact, I bought a too big house. Not too big for our paycheck, the cost and therefore the mortgage were well below what the bank qualified us for. Too big for the need. I paid for two rooms we really don't use.