> Do you think the people who would have been renting those properties simply vanish? Disappear from the rental market?

Actually yes, entirely unironically.

We even have evidence of this dynamic in Melbourne. When various tax measures were taken that sucked some of the profit out of investment properties, making landlordism less attractive, we saw there was less competition for house purchasing from well-funded investors. This in turn allowed would-be owner-occupiers to buy more houses, as they were no longer forced into rentals they didn't want, no longer outcompeted by those with easier access to larger lines of credit. This reduces the population of people seeking rentals.

Result - decline in the absolute numbers of rental properties in the city, but an increase in rental property vacancy and a slight decrease in rents.

> Any policy that reduces overall housing supply is a loss for the low end.

Except it doesn't reduce the overall housing supply, because overall housing supply includes both rental properties and owner-occupied properties. Those houses don't just disappear.

You're making the (false) assumptions that there is no interplay between the two markets and that everyone that lives in a rented house wants to live in a rented house.