... sucks to be them? No tax scheme is truly neutral, and any tax scheme is going to favor certain behaviors and disfavor others. If the behavior you wanted to undertake isn't the one a given tax system incentivizes, that's probably unpleasant, but somebody had to get the short straw, and as a society we may as well pick a short-straw-holder in such a way that broadly pro-social outcomes are maximized, like increasing the likelihood that more people have places to live.

Why not just raise existing taxes across the board to pay for this? Seems a lot more fair since pro-social benefits are distributed among the whole society.

The tax on income disincentivizes meaningful productive work. If you have to pay out $50 for every $100 you make, you would probably just not bother putting in the effort.

As grandparent said, every tax causes this kind of incentive. So people thought long about what was the least worst of all the options and came up with LVT and similar ideas. They cause the minimum harm to the economy and have the least side effects and "unintended consequences"