The reason for soaring home prices is that the equilibrium has changed with a sharp increase in external demand (Chinese and Russian immigrants, or investors).

Canada in general has become a desirable destination for people who have entered the middle or upper classes in their home countries, and are parking their new found assets in a country unlikely to revert to the socialism of the mid to late twentieth century. The recent upsurge in interest from Americans who feel they might be marginalized by the new Trump administration is going to cause this boom to persist for some time.

The BC foreigner housing tax does not entirely address the price issue, because the extra demand has not been eliminated (it has been reduced somewhat). Perhaps a better solution would be to require new citizens acquire ONLY newly built and UNDEVELOPED (or brownfield) property.  This would spur development, while leaving a base of housing stock for an equilibrium to be re-established.