Property taxes actually wind up being regressive a lot of the time. Having 2x or 10x income usually translates to a house that's less than 2x or 10x in value.
While you're partially right in terms of house property value, high property taxes encourage efficient use of land. They prevent wealthy landowners from just sitting on valuable land.
One other thing I forgot to mention is that the ultra-wealthy typically earn most of their money from investments, not income. This is why Mitt Romney pays a net lower tax rate than you or I and another reason why even progressive income taxes are fairly regressive.
State taxes often treat investment and wage income the same; particularly in California.
Formerly 15% + 0% (if you lived in WA) capital gains one year is now 20% + 3.8% + 14.3% (if you moved to California in 2013). That's a pretty big difference for the same gain.
That's not necessarily regressive, if a billionaire buys the same house someone making $70,000/yr doesn't make it regressive. It's not linearly progressive (ie 1:1 ratio of taxes to taxable amount), but is still progressive. Current income taxes (federal at least) are more regressive even though quantity of money might still be higher for higher income individuals.
I could be completely wrong, tax stuff confuse the hell out of me...
If the ratio of taxes to income isn't rising with income or at least keeping constant (which is what I think you're referring to as "linear"), your marginal tax rate is declining as income rises. I think you maybe mean it's staying constant with consumption, but that's kind of the problem - people with higher incomes tend to consume a smaller portion of their overall income, so taxes based on consumption are usually regressive.
That's pretty much the definition of regressive when it comes to taxes - people making more are being taxed less, proportionally.
"Land Value Taxes" are the solution to this. Taxes on the unimproved value of land, deterring people from holding huge amounts of land idly. Provide a way to donate land to environmental trust if you want it to be empty, or give rebates for certain pro-civic activities (i.e. a 100 year no-build promise on your land would reduce your taxes substantially)
