I think it would generally be just to allow the anonymous defendant to at least make a motion to strike out the claims while preserving their anonymity.
In this case we have a lot of reason to believe that the plaintiff brought the case exclusively to learn the defendants identity. E.g. Before bringing the action they offered $10 million dollars to acquire the domain, and have made threatening remarks. Not to mention no actual advantage is gained by removing the Bitcoin whitepaper from a single website, as there are easily found mirrors on thousands of locations all over the world, and since Wright's initial threats that includes the websites of several national governments, US congress, research institutions, and some of the largest financial institutions in the world (e.g. Fidelity).
This privacy invasion belief was only furthered when after the case the plaintiff refused to accept the ordered costs payment from anyone except the defendant and only if they identified themselves (also, after the case the plaintiff pretty much said as much).
Their case was seriously deficient too, e.g. falsely misstating that a US copyright registration was evidence of authorship even when the copyright office had made an unprecedented move of saying exactly the opposite in the matter of this specific case. Failing to disclose that there were other copyright registrants, failing to disclose that the supposedly infringing whitepaper was distributed under the MIT license and so on. Not to mention that there were major equitable issues, e.g. the whitepaper has been on the website pretty much since it was written some 13 years ago without issue-- placed there by its (actual) author.
Cobra wrote a letter to the judge and attended the hearing via zoom, and the judge took the position that he was required by the law to ignore the letter.
But at the end of the day the UK courts are powerless to protect cobra from harassment or even assassination so exposing his identity just didn't make sense. Particularly since Cobra is outside of the UK (or so I believe, no one in the bitcoin ecosystem seems to know cobra by any other identity).
And this is why you can't access the Bitcoin whitepaper at its original location or download the bitcoin software on bitcoin.org from within the UK today.
They're now seeing an additional nearly million usd worth of costs for their unopposed default judgement too. O_o