> It's strange that there is so much push back against foreign investment.
You say "foreign investment" as if they're looking to develop or improve the local economy and in the process make a profit. Many Chinese buyers have been targeting foreign real estate as a way to combat the fluctuations of their local currency, which is under suspicion of government manipulation. They're "investing" because there's nothing of long-term value in local areas, so they buy foreign properties in more stable markets. Without any consideration of the effect on the people living in that market.
> when foreign people want to buy something you have, that is called an export
Local goods that are shipped to foreign locations are called exports, and they're subject to significant extra taxation. Local resources such as land, water, food and energy that are bought and taken off the market to create shortages, thus increasing the cost of living for locals (thus increasing the value of your investment at the expense of others) aren't called exports. They're called market manipulation (or market speculation, if you're being generous).
> [Various comments about housing density]
Many of these properties lay vacant, which further drives up the cost of housing in already expensive locales. These buyers often aren't targeting areas for building commercial or high-density housing. They're buying multiple houses at the middle-class level, which contributes to an already vanishing middle class. The cost of houses and apartments in these areas has multiplied by 1.5x-3.5x the original value in a very short period of time. Unbalanced inflation like this perennial issue in the US given the lack of sufficient corporate oversight. Artificial inflation (beyond currency inflation) of the cost of living should be the prime issue for any major city.
Allowing them to buy and sit on valuable land that could be developed when they have no intention of development actually prevents us from increasing housing density in these high-demand areas. That's the whole reason they're introducing this tax. As long as there's some sort of time-limited exemption for actual construction and development that will cover people building new commercial and high-density housing structures, it's exactly the sort of thing we should be doing with our rate of population increase.
> rents were more reasonable in Tokyo
It's also perniciously difficult to rent in Tokyo as a foreigner. And when moving into a new apartment, locals will often pay a move-in gift of 3x the monthly rent as a tradition from post-war shortages. Japan also has a much more advanced public transit system, allowing for longer commute times and more stable pricing. China also doesn't allow foreigners to buy land or open businesses. In any case, Vancouver's and Seattle's current unreasonable rents are a factor from external manipulation, so once we curb the foreign investors who don't develop or use property, it should become much more competitive.