The perpetrator remains anonymous while the victim will be doxxed, what a great sense of fairness you have.
So in the US, at least, if you're going to sue someone over IP violations, you should plan on your identity being made part of the public record. As a country we're pretty adamant about that. It's a feature, not a bug.
I'm including DMCA notices in things I believe should be -- must be -- transparent. They're legal filings after all, strongly implying that if you don't comply, you're about to be sued. Your proposal would allow, say, Oracle to hide their identity if they were filing a complaint against the Linux kernel so that they could get the benefit of launching a legal salvo without the reputation hit for having done so. I believe that's far more unfair, and more likely, than your scenario.
Curiously, Github seems to understand that.
But DMCA is a US law.
You can request the data from the courts, or whatever. It's not Github's job.
The notice and takedown part of DMCA was a reasonable attempt to address a real problem. The main flaw seems to be that bogus takedown notices are never prosecuted, so there's a lot of abuse.
I don't have as much faith in the system as you, apparently.
Sometimes the DMCA'd person is the victim, and the complainant is the perpetrator. What is your response to those situations?