> We don't do this because of principles, because of the risk of enabling other crimes, and because it would be a bad tradeoff
Really the only reason we don't do this is because of the Constitution. The Constitution could prevent us from capturing beneficial ownership data from corporations, but indeed it does not. Of course one can make this argument in front of SCOTUS (and perhaps will some day) but there's a reason you're not making that argument now, which is that it's a bit silly on its face.
Corporations are fundamentally legal objects of the state, which is why they're registered at all. You can operate whatever business you want without incorporating (and without the legal affordances thereof) and then you don't need to disclose any information to anyone.