Also, did I understand you correctly as agreeing with me that a collection need not be Iterable?
If so, that means that Deque, Stack and Queue are not Iterable by default. One may provide an Iterator (or do you believe you shouldn't be able to); but if you don't, you can only use their default Interface which doesn't include one - thus confirming our restricted access Policy.
I think I agree with you, however I'm arriving at this position from a different direction. My logic starts with real-world observations.
We've agreed that without Tags the
isOrdered property is not applicable. Thur, the only order possible in an unTagged collection is the implicit Ordinal order established by the relative, temporal order in which Items are entered into the collection. We have also agreed that Iterators operate on the collection's Ordinal Order. Now, if I can find just one real-world case where a default iteration does not work properly (i.e., return Items in their Ordinal Order, or some function based thereon) then I can say that the collection is not
inherently iterable "out of the box".
On Saturdays, everyone in our village goes grocery shopping and the queue at the meat counter becomes quite crowded. The butcher attempts to remember our Ordinal order and iterate across the customers in a fair and orderly fashion, but (to the butcher) the customers in the queue appear to exhibit Brownian Motion as they socialize with each other during their wait. As a consequence, I have noted with dismay that customers arriving after me are occasionally served before me.
Now, at the PIM level, we design our queues with a memory device to keep track of a queue's Ordinal Order. In fact, using a computer built with today's technology, forces that upon us. thus all collections are iterable in a PIM. But, at the CIM level not all collections come with a memory device (such as rope enclosed isles) to retain the Ordinal Order of its Parts.
After much grumbling by the customers, the butcher installed one of those machines that dispenses sequential number tags as a surrogate memory device. But that converted the queue to a Tag Ordered Set.

Thus I arrive at the conclusion that collections, at the CIM level, have faulty or non-existent memories and therefore need Iterators defined for them.
I'll go on to say that, in addition to providing access to parts in a collection, iterators enforce access rights to the collection.