Even under the best circumstances where the ring0 anti-cheat developer is not malicious - which I'm absolutely not convinced is always true, mind you - they can be exploited by bad actors to take control of your system via privilege escalation. This isn't even just a hypothetical, it's already happened with basically all that are commonly in use - EAC, GameGuard, BattlEye, XignCode3 all come to mind. It's just bad opsec to run games that use them. You could be doing everything else right with securing your machines and network, and it won't matter. It's leaving the back door open.
I'm curious if an open-source anti-cheat consortium would be successful, or if this is one of the few cases where security through obfuscation might be the only way to protect anti-cheat software.
I don't think it would be possible tbh. You are correct in that security through obscurity is the only way these client-side solutions work. There are some amateurish open source anti-cheat frameworks but with the source available everything is easily disabled or bypassed. The only true solution to cheating that isn't invasive is implementing robust server side checking and active human (or hell, even AI could be used for this...) monitoring of anomalous player activity.