it's actually a wealth tax, not an income tax
Wherein lies the problem with our tax system. Were it not for rich folks making all the rules, we'd not have had this silly "income tax" notion in the first place. It's pretty much the very definition of a tax designed to prevent upward mobility.
A wealth tax assumes liquidity: for instruments such as REITs where the underlying asset is not itself terribly liquid (imagine, for instance, owning a shopping mall outright), how does one go about liquidating such a thing in part? Finding another partner? And then the next year, when the same thing has to happen again?
In a property tax system, you do not have to pay the tax on your basket of oranges by taking oranges out of the basket. You can just as easily pay it with apples from your basket of apples. If a person has unwisely accumulated a disproportionate amount of illiquid wealth, they would just mortgage some of it, or the government could assume an ownership share. However in such a system, people who knew they would be paying tax each year would avoid doing so, and this is a good thing, because it provides disincentive against destructive asset bubbles and encourages productive use of property.
Finally, the issue remains of incentives. France has a wealth tax, and the net result of this is that while it has collected $2.6 billion (equivalent), it has resulted in $125 billion in capital flight since 1998
Yep, other than the government being owned wholesale by the rentier class, the real problem is here, you nailed it. For the forseeable future, there will always be a sovereign entity that caters to wealth horders' needs, so any move towards a property tax system would have to be accompanied by some rather ingenious legislation and enforcement (and when is the last time you saw that happen?)
The other big problems used to be the intrusive measures necessary to prevent the hiding of wealth and the giant bloat of the accounting industry such a system would produce, but since we have an engorged financial/accounting sector anyway, and the government and corporate institutions seem hell bent on making privacy a thing of the past for reasons of control and profit respectively, those are no longer obstacles.