There are a lot of factors at play here, not just the immediate health risks to the player. I can't see how Fyfe staggering off was a good look, or could in any way be seen to minimise any further injury, but I am not a health professional, so that is just my "armchair" opinion.
But additionally, there has been a lot of focus on head trauma in professional and amateur sport recently, and the incredible dangers in players playing on, or coming back too early. This is increasingly true in kids sports as well, and there is the whole role modelling debate about playing with injury - Insight did an interesting panel discussion on this a few weeks ago which is worth a watch. Among them was a neurologist who talked about the increasing risk of adult injuries in children due to the increasing professionalisation of children's training, and these included concussions.
At a time where we are (as junior admin and coaches) desperately trying to get the message across that there is no such thing as a minor concussion, and all head and neck injuries should be treated as severe unless proven otherwise by a suitable qualified health professional (noting that this does not include physios), I think it sends a disturbing message to see a player who is evidently severely concussed stumbling off in the arms of trainers.
Unless the player can clearly walk of their own accord, I think that there should be a mandatory stretcher rule in the AFL - as much as anything so that it sends a clear message through amateur and junior ranks that head trauma is always potentially serious, and should be treated accordingly, no matter who you are or where you play.
That probably makes me part of the nanny state. So be it.