From Reason:

Given that guns with serial numbers are indeed, as the court pointed out, just as effective at self-defense as guns without, the serial number requirement seems to me to be a much lighter burden than the burden of objective, easy-to-comply-with licensing requirements, which the Court in Burden endorsed. True, the serial number requirement does interfere with the privacy of gun transactions and gun ownership, and privacy hawks may be concerned about that. But of course the shall-issue laws upheld in Bruen also interfered with the privacy of gun carrying, since people would need to identify themselves to the government to get the license.