We should reward the person who lives in a normal house below their means, and buys an apartment as an investment (which is private capital into new construction that wouldn't have happened if they didn't do it), then rents it out, which increases stock on the rental market, and decreases rental yields.
If you want to tax ALL housing the same, including people's only house, then sure, go for it. Or better yet, tax all land ownership. Just don't distort people's behavior by making a special exception for their main house.