I still think the easiest way to solve the lack of housing issues would be to charge an override premium interest level for second homes and investment homes.
Make it unprofitable for landlords to carry the costs, and voila, more homes on the market.
That, or reverse the taxability of interest on homes. Primary residence? Interest is deductible against earned income. Investment property? No tax breaks on interest paid, only capital improvements. This would also be a huge cost-of-living improvement for lower and middle classes.
Would make for a lot of unhappy boomers with multiple rental properties, but honestly fuck em, they've had a good enough ride already.