The UK has common law: the outcomes of previous court cases and the arguments therein determine what the law is. It’s important that court records be public then, because otherwise there’s no way to tell what the law is.

It is the outcome of appellate court cases and arguments that determine law in common law jurisdictions, not the output of trial courts. Telling what the law is in a common law system would not be affected if trial court records were unavailable to the public. You only actually need appellate court records publicly available for determining the law.

The appellate court records would contain information from the trial court records, but most of the identifying information of the parties could be redacted.

There are middle grounds - for example you could redact any PII before publishing it.

It should be possible to redact names from cases for that purpose.

It should be possible to leverage previous case law without PII.

> It’s important that court records be public then, because otherwise there’s no way to tell what the law is.

So anyone who is interested in determining if a specific behavior runs afoul of the law not just has to read through the law itself (which is, "thanks" to being a centuries old tradition, very hard to read) but also wade through court cases from in the worst case (very old laws dating to before the founding of the US) two countries.

Frankly, that system is braindead. It worked back when it was designed as the body of law was very small - but today it's infeasible for any single human without the aid of sophisticated research tools.

That can be solved by migrating to a sensible legal system instead.