Usually the information has to be public is the registering entity is a company, and can be private (and I think it’s by default) if it’s by an individual. It shouldn’t be possible to have private company registrations. This of course depends on the TLD, but might have implications on some jurisdictions independent of that (like when using a site of any TLD inside the EU).
While I fully agree with the SSD side, you seem to ignore that HDDs are also getting cheaper per TB (always have, and usually quite noticeably). Also the reliability of large to huge SSDs remains to be seen as well. Obviously a breakthrough in HDD technology would have an influence as well, as you mentioned.
I’m not saying SSDs aren’t here to take over, they surely will eventually (preferably sooner), but I think it’ll be a few more years until we got actual price parity per TB. Even when ignoring other aspects like reliability.