It may be that I'm just a newbie, but...
Why can't Possessor demons have Boost? What about in the Exorcist, where the possessed girl had superhuman strength? Also, biblically, there is an instance of a demon possessed man who kept breaking chains they put him in.
Am I not thinking correctly about how Boost is supposed to work? Or is the Demon's stamina used instead of the possessed individual?
Hello,
Welcome!
Your final question is your answer: all those examples concern (in game terms) the demon's Stamina, not the hosts. Boost would give the extra Stamina to the host for his or her use, which is not at all what Possessor demons are doing.
Also, since the demon is indeed housed in the host's body, the host's Stamina may be strained beyond its capacity if the demon's Stamina is stronger. Therefore being possessed by a demon who uses quite a lot of Stamina is very dangerous to the host's health - and you can see, I'm sure, how that fits perfectly with the events in The Exorcist.
Best,
Ron