Companies should not be allowed to have secret ownership; I don't give a shit if this data is leaked. Corporations are a legal fiction, and so they have no right to or expectation of privacy, like there should be for persons with e.g. individual tax records.
The basic operation of markets depends on having as little information asymmetry as possible between opposite sides of a transaction, and part of that means knowing who you're doing business with to make informed decisions about the reputation of your counterparty.
You are of course free to decide whether or not to do business with an organization based on how well you know/trust the ownership, and decline do do business that are evasive about their ownership at your own prerogative.
I'm not sure why ownership needs to be openly published in advance -- you can always query them confidentially through private correspondence -- or how having ownership compiled into a federal database that you don't have access to (unless you have corrupt influence over the relevant agency) will help you.
The basic operation of markets depends on having as little information asymmetry as possible between opposite sides of a transaction, and part of that means knowing who you're doing business with to make informed decisions about the reputation of your counterparty.