> The tax deduction is nominally smaller than the equity you would gain on an equivalent amount of money going to principal rather than interest.
True, but you can't ignore the "choice (3)" that you mention. I'm not in the market for a house right now, but if I were, I would absolutely get a mortgage even though I could pay cash for the whole thing. It's a non-zero risk, but I feel it's a reasonable bet to believe I can make enough in the markets to more than offset the mortgage interest, especially with the MID in play reducing my overall tax.
That doesn't really address the point the parent was making about buying a house being a good tax shelter (I agree with your premise if you restrict thinking to just that), but I don't think it's safe to ignore it in the bigger picture, either.
If there are people out there "sheltering" themselves from taxes by paying more in mortgage interest, those people are idiots. Any savings you gained on taxes were already wiped out by the fact that you effectively threw away money on your home (i.e. your money did not go into equity; to you, the money just went into a black hole).
I understand that they pay less in taxes as a result of mortgage interest, but if you have an actual choice between (1) spending $1 on mortgage interest and getting a tax deduction or (2) spending $1 on principal and not getting a tax deduction, the choice that leaves you wealthier is #2. Obviously this is not how mortgage payments work and ignores choice (3) of putting money in some other asset, and the time value of money should be considered, but for each equivalent dollar, I would rather get more equity in my home than a tax deduction. The tax deduction is nominally smaller than the equity you would gain on an equivalent amount of money going to principal rather than interest.
This isn't even considering the extra costs of homeownsership, especially property tax and maintenance (and the latter is tax deductible to a much smaller extent than mortgage interest).