I actually tend to agree with both sides on the general principle. Yes having foreign buyers in the market increases total demand and thus raises prices, but it also puts more money into the system which can prompt more construction. And if construction keeps pace with demand then that will equalize prices. It's the classic supply and demand curves. On the
supply curve, the quantity of supply increases or decreases based on the price point.
If some of the homes remain empty, more total supply is needed to house the population, but that also means more money coming into the system. And with taxes on vacant properties, this both reduces the number of properties left vacant and injects additional money into the government to counter the harm, such as through housing/income subsidies.
The first snag is if it isn't possible to provide the necessary supply for some reason. If there are shortages of land, labour, or building materials needed due to regulatory or macro economic factors then the prices just keep rising since there's no relief valve (inelastic supply). However, if one or more of these reasons make it impossible to provide sufficient supply then yes, placing controls on demand is the next best option. It's like, the water level of a dammed lake keeps rising if the outflow valve can't be opened wide enough. Problem is, there are still so many regulations pertaining to housing - often related to exclusionary zoning - that I'm not convinced that the "relief valve" has actually been opened to full capacity.
The second snag is that even if the number of units supplied is higher at a higher price point, the demand isn't coming from everybody. If 🞵🞵 units are supplied at price $$ while only X units are supplied at $ price, there may be more units supplied at $$ price than $ price, but it's only by people who can afford to be $$. So the greater number of total units supplied at price $$ doesn't necessarily do much to address demand from people who can only afford $ since the supply and demand curves intersect at $$ rather than $. That's why some housing experts argue that the issue is largely on the demand side because of the increased level of wealth/income inequality now compared to in past decades. Much of the supply capacity is exhausted by demand from people (whether foreign or domestic) with higher wealth levels. But of course, if supply capacity were greater, units would could be supplied at both $ and $$. Just like say, a phone maker will sell phones at both $1000 and $500 if it can, if it only has enough capacity to satisfy demand for the $1000 phone, then those who can't afford that do without.
So technically there are potential strategies on both the supply and demand sides.