The reason why people spend 65% of their after-tax income on rent is because people are willing to spend 65% of their after-tax income on rent. Supply and demand is a bitch, and when you fuck with it, you create massive distortions that end up enriching a small minority at the expense of everyone else (for an example, see anyone paying $600/mo for a nice 2 bedroom rent-controlled apartment in Manhattan).
And I like the idea behind a progressive property tax, but it would never, ever, ever become law in the US. Not while there is a single breath of life in any lobbyist or congressman.
If you want to see how sick accommodation can get you don't have to look further than Japan. House there is such a valuable asset that it's often shared between three adult generations. And if you have to rent an apartment you often have to pay additional half a year of rent up front as a non-refundable gift to the landlord. http://en.wikipedia.org/wiki/Key_money
I think government should try to put as much of the real estate in hands of as many different people as it can.
I'm not saying government should hit families that own two or three apartments or houses and rent some. I just don't like the ones that hold dozens of properties (lots of them empty) barely keeping them from falling apart. That's no good to anyone, apart from them.
You buy apartments and charge people significant part of their earnings for the privilege of having a roof over their heads.
Why is that bad?
As an owner you don't live there yourself so you only have an incentive to keep the place in shape good enough to be rented. Which is usually pretty low.
The worst part is that if you can't find the people to occupy your apartment your costs are pretty low (you don't have a profit but that's not the same as money being drained from your account). So you can buy and hold apartment for years at very low cost. This creates artificial scarcity (in addition to actual scarcity) of places to live that keeps the prices up.
I think progressive property tax would enliven real estate trade. Prices would drop and more ordinary people could afford to buy one on credit instead of renting. This could save working people a lot of money so they can actually start their lives instead of slaving on their first job with just enough money to pay the rent.
Tax should be constructed in such way that holding even large apartment, or even two or three would pose no burden or almost no burden, but you might be better of selling your fifth apartment even at 50% below market price than holding it for a year.