An incapacitation of any crew member is an emergency situation. The same for a medical “emergency” with a passenger.
One of the simple reasons being is that as we are not qualified doctors we cannot certify that the person is dead. Declaring an emergency gives you unconditional priority over everything. Can you imagine not declaring an emergency and having to take up the hold for 20 minutes, receiving a convoluted taxi clearance, then finding out if you had actually got on with it the person may have lived?
Also with the crew, if the Capt dies (or F/O) you are now in a single crew environment in a multi-crew aircraft, even if you have a relief F/O in the other seat. I’ve flown left seat in the sim when I did my Chambery training and it’s a weird environment, I had to do a circling approach to land and the biggest thing that breaks down is the instrument scan. Apparently it takes 6-8hrs of flying to get used to the left seat again.

Dean