Most people underestimate the harm of that program because they don't understand price elasticity. It's true that only ~1-2% of apartments are under that system. However, 1-2% supply destruction can actually double prices. (See: oil shocks.)
Another problem is that this country is run by scumbags and pussies who allow foreigners to own real estate (many countries don't). Now, I'm all for a reasonably open immigration policy, and letting foreigners live here is not the issue. (The people who move here to live here don't have a major effect on the rent, and are good for the country overall.) But the types of foreigners who buy U.S. real estate are usually corrupt officials who want a place to live if their own country brings them to trial. (In China, corruption is a death-penalty offense.) This is the real reason why Silicon Valley is so expensive: every fucking Communist Party scumbag in China and murdering Russian oligarch and Arab slave state billionaire has bought a place (even if it goes uninhabited) in California. It doesn't affect a large number of houses, strictly speaking, but it's enough of a margin to have massive impacts on the price level.
I am amazed at Americans' willingness to be "patriotic" about stupid things and get into nonsensical wars... but then we go and let corrupt, murdering dictators and billionaires from all over the world buy California and Manhattan real estate. It's fucking disgusting.
The other thing to think about is, do you really think "communists from china" are buying 1-bedroom apartments in the Mission? No, they are buying the multi-million dollar homes in Russian Hill. For the average American those homes were never within budget.
http://www.theglobeandmail.com/news/british-columbia/scant-e...
I think you could argue that foreign money is driving up home prices in Vancouver, but it's certainly not the main factor raising home prices.
The problem is people. People usually fight against "ugly" new development and "Manhattanization" and change of all kinds, and while they make arguments based on urban beauty, they're really just trying to protect their obscene premiums on real estate by blocking new supply.
I actually think urban home ownership makes no sense for most people. Ownership is about a sense of control. If you live in the woods and sit on an acre of land or two, you can be pretty sure that no one's going to block your morning sun, or set up a nightclub next door. Cities can't afford to grant those assurances. It's just better, from that standpoint, for most people to rent. Why make your primary investment something that another person with more power and more money can easily fuck up, just by buying space near it?