What do you think "dying" means, or looks like? What signs would such a "dying" awake person display, that a "dying" sleeping person wouldn't?
Choking? Pulse goes up and breathing becomes shallow.
Cardiac arrest? Aneurysm? Torn blood vessel? Shot in the head? Stabbed in the chest? Poisoned? Spider/Snake bite? Fell off bed and broke hip? All these "dyings" are easily detected by pulse and breathing monitors.
"and it's much easier to detect the neurological symptoms of this in a patient who is awake"
In this context, I imagine neurological symptoms would be things like cognitive function, spatial coordination, memory functions, and linguistic functions.
All of those are things that are not really possible to assess while sleeping, but would be possible to assess in a patient who is awake.
Cranial bleeding can be caused by blunt head trauma, can raise intra-cranial pressure high enough to kill you, and there are only three ways to detect it: a) medical imaging scans, b) changes in patient behavior, or c) drill a hole in the skull and insert a sensor.
If the patient is sleeping, you can't use a) or b). Now, there might be an argument that everyone should get c) and lots of sleep, but drilling into a person's head is not risk-free either.
Choking? Pulse goes up and breathing becomes shallow.
Cardiac arrest? Aneurysm? Torn blood vessel? Shot in the head? Stabbed in the chest? Poisoned? Spider/Snake bite? Fell off bed and broke hip? All these "dyings" are easily detected by pulse and breathing monitors.