With that in mind, if you fork an organizationally-managed repository, there's a good chance the owner doesn't want you to continue to have access to that codebase if you're no longer a part of the organization. And the local copy? Well there's a good chance you were only allowed to clone the repo on an IT-managed device with specific 2FA policies and some kind of agent/config to prevent/reduce data exfiltration from that device.
Is it a perfect system? Hell no. Data leaks, that's part of life. And I'm with you that it certainly could be more user-configurable.
But it's also extremely well-documented behavior[1], and seems like a key design choice that GitHub made a long time ago to protect the owners of private repos. Ultimately, if you don't care about who has access to your code, you signal that by making the repo public. Or by telling your private collaborators to make sure they hold on to a local copy.
[1]: https://docs.github.com/en/pull-requests/collaborating-with-...