Because foreign investment in real estate can massively distort prices for domestic market participants, which can lead to a variety of other negative affects for the communities affected by that investment.
One could argue the same applies to investment properties by Americans who do not live in those communities, but it seems like an acceptable line to draw I suppose.
Same applies for the stock market (foreign money is pushing it up, increasing the costs at which retirement funds purchase equities). But yeah world's finance is heavily interlocked.
Not really the absolute price of stocks isn't so much of an issue though the only thing that really matters is how much it's growing for things like retirement funds and investing. A house however is a pretty indivisible unit, splitting or sharing a house among many owners is really unusual outside of houses built for that purpose. On top of that not everyone has to own stocks (somewhere over 50% of American's have no stock holdings not even in retirement plans) but everyone needs some kind of home/shelter, be it rented or owned.
They simply don’t have the framework to regulate those kinds of things, however. And it doesn’t really fit with the economic liberalism that has been pretty constant since it’s founding.
It is kinda weird though - if an alien race basically arrived with trillions of gold bricks and started buying US properties (and obviously not showing how many gold bricks they had or that they were aliens) there would be an effective take-over of the country. There would be absolutely "rich" people with gold bricks in their trunks driving around realizing they can't actually buy other homes. edit - I'm talking about space aliens because hey ;)
One could argue the same applies to investment properties by Americans who do not live in those communities, but it seems like an acceptable line to draw I suppose.