AWIL: Exorcist also took a few years to get, and the wolf puppets are already built and still around, given how we see them reused nearly every year at this point.
Freddy vs Jason: Exorcist was also used at Horror Made Here, so don't see the difference there.
Poltergeist: Point still stands.
Exorcist took a few years to get initially, but we can assume that they have a good working relationship with the rightsholders, which may have been improved further thanks to blumhouse working on that new sequel/reboot. As for the puppets, I haven't seen anything to indicate that they keep and reuse the same rigs, rather than rebuilding and modifying them year to year, especially since they have to make new skins for them pretty much every time anyway. Not to mention that it seemed like Landis and the AWIL rights holders were a bit more hands on with quality control and the design than the exorcist ones, which could be more effort that the corporate heads wanted since its supposed to be a quick replacement as is.
Exorcist was used in horror made here because Warner Bros distributed the movie, but they dont own the rights outright. New Line, who own freddy and jason, is a wholly WarnerMedia company.
Didn't see you initially mention poltergeist, but i think the main conflict there would be cost, since the demands of the set and creature effects were quite a bit more extreme than Exorcist, making Exorcist the cheaper option for just as much if not more than Poltergeist for public recognition.
Given Murdy's implication that this wasnt a choice made by the design team but rather the corporate heads at universal, I think you need to look at it from the perspective of what costs the least, will take the least time to build, and has the widest public recognition, rather than what would be the best recieved or best maze from an artistic perspective.