[labcomputer]

System Integrity Protection (SIP)[1] does prevent even the root user from modifying some system files[2]. It seems possible, at least in principle, to protect system logs from modification by user root. In practice, I think most system logs are stored in /var, and that part of the directory tree does not appear to be protected by SIP (but I hope I'm wrong!)

[1] https://support.apple.com/en-us/HT204899

[2] Unless/until you reboot to a diagnostic monitor on a special partition (which requires pressing command-R from a local keyboard during the POST), then run a command to disable SIP, and then reboot again. Continuity Activation Tool requires users to perform this step as part of the install process to allow installation of Bluetooth drivers not originally signed by Apple.

[marctrem]

A motivated and knowledgeable adversary could most likely load a custom kext to bypass the integrity measures. Am I right?

[nothrabannosir]

You can't load unsigned kexts anymore, due to that same SIP. It's a pain in the gonads when hacking your own kexts. I had forgotten about this, but it does indeed allow for a system that leaves an audit trail which cannot be hidden, even by root.

However, user labcomputer is right, I doubt that applies to the solutions proposed by OP here. Well, I'm certain: root can switch out the shell or terminal emulator binary itself and have it lie about executing those commands and return something trustworthy. One way or another, to truly check this, you'd need an immutable audit log (probably not currently available), AND a reboot into safe mode or a mount as a HDD onto a safe system.