I find that idea especially strange in light of the new tax laws that force Americans living overseas to pay income tax back home. It's seen a record number of Americans relinquish their citizenship so far this year: but if that citizenship can't really be 'relinquished', what difference should it make?
Oh, you don't have to pay taxes while it's relinquished. The point is that you can get it back whenever you want it.
Americans living overseas are permitted to earn a certain amount of money tax-free anyway, and it's a fairly substantial sum. When I was in Saudi Arabia in '07 it was around $58,000 a year; now it's probably higher. After that you only pay taxes on the difference. And, of course, if you're living overseas there is really no way to prove how much money you make. The IRS can't demand W-2s from foreign employers. Well, I guess they can try, but it won't do them much good. So it's still pretty easy to hide your money overseas.
I'm not sure what stateless individuals do when they're traveling. I think I read somewhere that they can get a travel document from the UN which essentially works like a passport. They'd still have to pay taxes wherever they were living, of course — assuming that place has taxes. A lot of them set up house in tax havens like the Cayman Islands for that very reason.
You don't need a passport to buy property, just money.