There are exemptions available to members states:
https://ico.org.uk/for-organisations/guide-to-the-ge...
On the fence on this. In an honest world, there's no need to hide the registrant's name. In the real world, people use this information to 'go after' the registrant either online, or literally in some cases.
Consider the political world, where people with a point of view get targeted by opponents' online muscle-men. Or consider fake news / propaganda sites where one person can create multiple sites, which reinforce one another on a political point of view, making it appear as broad support or opposition. In reality, little will change in this sense. Political, net-savvy people get a domain management company to avoid going public.
I'd make an exception to political / religious / sport sites, in that the registrant has to publish their name, address, and where they plan to be at the weekend. Get the ideological trolls off the web.
(or at the very least, let people join the dots on who is making these sites, and who is funding them)