Foreign oligarchs affect supply, and I don’t think we have any idea how much. Corporate owners are probably a bigger chokepoint on supply, but domestic wealthholders are probably a big player as well. We need a variety of rules in place; enforcement of any of them will increase supply, but that mostly benefits whoever’s left in the list above. If we crack down on the biggest supply problem, the next biggest one will buy up the excess.
If we actually want private homeowners to take precedence, we have to make it extremely difficult for anyone to own multiple homes, corporation or not, wealthy or not, foreign or not.
To your point, this rule, whether it becomes an enforceable regulation or not, isn’t even targeted at increasing supply. It’s targeted at preventing money laundering.