As if there aren't legitimate, legal reasons to hide things from the government. Have they earned any kind of trust? Have they not been breached by hackers hundreds of times? Has law enforcement in the USA specifically proven themselves trustworthy?

Cops are substantially over-represented among domestic abusers so if this is an effective tool for victims then this would still be a concern.

Whether or not it's effective should be pretty easy to check since this is already legal in some states but not others. Or it should be much easier for abuse victims in the US compared to e.g. Nordic countries where corporate ownership information is fully public. Since I find no evidence of such a difference it would seem this is just the usual case of rich people using actually disadvantaged people as a cover for their bullshit.

(Though I feel like there's maybe a more direct solution to this aspect, maybe something with a nice slogan you can chant at marches...)

Yeah, innocent people hiding from the police isn't the right solution.

I can't find anything in the law which restricts disclosure of the information in any way, much less makes disclosing it a crime (as it is for tax returns, for example). Is there some thing I'm missing?

I guess the answer is in here somewhere but I'm not qualified to interpret it:

https://www.fincen.gov/foia-and-privacy-act-guidance https://www.fincen.gov/foia-exemptions-and-exclusions