Here’s a different take that’s trying to be a bit more generous to the OP.

The goal isn’t necessarily about reducing home prices, it’s about increasing home ownership. Those shouldn’t be conflated.

So if that same context was applied to evaluating education, it has worked as the overall educational attainment has increased. Whether the cost is worth that increase can certainly be debated.

From the comments I'm reading, many just want a progressive tax applied to investment properties. I don't see a downside to that.

On the margin, that’s likely to reduce the supply of rental properties at a given price. Whether that’s good or bad on balance is an open question, because renting is clearly advantageous for many people, while ownership better for others.

I assumed it would not apply to multi-unit properties but only to single-family houses.

Around here (Cambridge, MA [and Somerville]), a very typical rental is in a 3-family, sometimes a 2 or 4 family. It’s fairy unusual to be able to rent a single-family here (there aren’t very many available for rent).