There will still be a lot of people homeless even with affordable houses since they most likely cannot afford a house. Social housing doesn’t have to be affordable, it just needs to be there, but that has little to do with the availability of houses and more the amount of people that can be processed by the system. At least in NL.
The issue all around the globe is people owning more than one house. You can only live in one so they rent them out. Generally asking way to much since they took a mortgage for it, costs are deductable against the profit. So you always end up paying the mortgage rate for the house you rent + a profit margin for the owner.
If you stop people having 2, 3 or more houses or at least make it a lot less likely for people to own more than one. In NL some people are also debating if we should remove the deductibility of mortgage rates.
Houses costing 1m or more being empty doesn’t do anything for the homeless, they will not be able to afford that. A lot of the houses in the empty house statistics are include houses being built/renovated/destroyed etc. Heck in the US (and other countries) you have some ghost towns, are those counted as well? Or houses that are rented out for tourists? How many of them where empty for more than 6 months?
Taxing empty houses is fine, don’t get me wrong, but the not building medium density houses, places where you can walk and/or bike and actually want to live, the lack of social security and people owning 2 or more houses are issues as well.
People have overbid 10-20% or even more here in NL in the last few months for all kind of houses and apartments. Including once that need a ton of work.