I believe the host is the one who always gets the shards and other fallen spire event spawn stuff. As that stuff is not giftable, that basically means the host is stuck with the perks and the responsibilities of the fallen spire stuff. The foldouts are pretty much the only way the other players will get to benefit.
I think there might be a suggestion on the bug-tracker about allowing fallen spire event stuff and the other hub structures to be giftable, but I don't know.
EDIT: Actually, now that I think about it, it is actually player 1 who gets the fallen spire stuff, not necessarily the host. Usually, player 1 is the host, but if you exchange save games and change who is hosting, then it is quite possible for the host to be someone other than player 1.