A few hundred MLS groups is a lot of state for a phone to carry. Each group keeps its own ratchet and its own member list, and after a restart the client wants to reconcile all of them. That is why the cost shows up in sync and not in sending. Loading group state only for the chats on screen would flatten startup, at the price of one short fetch when you open a new one. The harder half is storage, because a thousand small encrypted records is the shape Android's file layer handles worst.