Some "private" data _should_ be public domain!
It seems to me a basic right in an open society to know whom you are doing business with.
GDPR has many advantages in protecting individuals, but it's also having a lot of unintended consequences. I used to belong to a forum for former staff of a large organisation. It was a great place where memories were shared, a resource for researchers (of that industry's significant history) and ex-colleagues alike. Many of the contributors are no longer alive.
Now its gone, as the costs of GDPR compliance were simply too great for the private individual who set it up. Much of the data was >40 years old though, with almost nothing from the last 20 years.
There will be a lot of stuff like this, I fear.
Then there's Companies House: I do a lot of research using its data, mainly competitor and (potential) client analysis. It's essential for our business to know who you are dealing with. Never mind GDPR, laws on filing company records have been "relaxed" over recent years, especially for smaller companies (typically fewer than 100 employees, which is our target market), to the extent that you can now learn almost nothing from what CoHo keeps. In particular the "balance sheets" they now ask for are a joke. By the time you've chased down the ownership of small companies, sometimes nested five levels deep, you've a good idea if they are trustworthy (or not), but you also need to be able to spot that a company is on its knees, before you extend it dangerous amounts of credit.
I think all limited liability enterprises should be required to put director information and _full_ accounts into the public record,as a condition of trading, and that late filings and holding stuff back should actually be penalised (rather than the pretense of same). If we want moral superiority over say the Russians or even the Americans, it starts with as much transparency as we can manage. And the more honest our society is, the cheaper it is to run, and the more attractive we are for others to do business with.
Back on topic, Whois long ago ceased to be very useful. Tried complaining recently to a contact point for some small-but-annoying site that's badly set up (or insecure or whatever)? How far did it get you?
What's wrong with an anonymising referral system, like those Usenet servers in Finland*? Let ICANN or whoever pass through the data, but unless something is escalated, there's no need for actual names to be sent to the complainant. It's not hard.
*You probably have to be of a certain age, and/or frequenting the wrong newsgroups...