I think that's correct in principle, but the important difference is that you don't have to know the priority in advance. E.g., to implement an Israeli queue u

I think that's correct in principle, but the important difference is that you don't have to know the priority in advance. E.g., to implement an Israeli queue using a standard priority queue, you'd have to track the priority of each "friend group" in a separate data structure. Concrete priority values are also difficult to reuse without accidentally inserting a new group in the middle of the queue - so the values are at the risk of overflowing.