If the direction this is going towards is true:
“Brig phys is not a doctor and is not part of medbay”, while at the same time they are limited with medical gear.
Then you should move the brig phys closer to security team as a combat medic, which should participate actively with security.
Otherwise you are just removing tasks for a role that already has barely anything to do. From my experience a brig phys for the first 40 minutes tries to prepare for (Future incoming patients), which if limited by medbay, will be even harder.