The weird thing is that this really is within the realm of the possible — the UK, for instance, abolished mortgage-interest tax relief in 2000, a move which had no visible effect whatsoever on either house prices or homeownership, but which did wonders for the exchequer.
But here, again, political institutions come into play. The US and UK are similar societies in many respects (as far as these things go) but we have very different political institutions. Something like the mortgage-interest tax deduction thing is basically a case of ripping off a band-aid. A government that went ahead and did it would face an outcry, but most people would wind up better off soon enough and there’d be no good reason to put it back in place.
The American legislative system, however, is not a good venue in which to attempt to rip off a band-aid. Nobody wants to propose such a thing, provoke an outcry, and then have it not happen. And the odds of getting 60 votes in the Senate for anything more controversial than a vote in favor of mom and apple pie are pretty thin. Consequently, bad policy can just sit there on the books with everyone afraid to peek their head over the ramparts lest it get shot off.