The EBF module can be inspected, and EAC won't have kernel access, so that limits it significantly. Things like crowdstrike, completely hiding it's processes, etc shouldn't be possible without it having kernel access.
The systemd service can easily be confirmed to only run while a game is running as well. You can even restrict the service to be masked except when specific games are running.
EAC having root access is a valid concern though, it will have full access to your entire filesystem. Normally you can restrict what files a systemd service can access, so we may be able to quarantine this to block any privacy concerns. However we'll have to wait until it comes out to know that part.
Overall it's not perfect, but users will have much higher ability to audit it on Linux versus the Windows version.