Another way of thinking about this, maybe, is that “unordered” collections are currently “ordered by added datetime”. What’s different (from the pov of the user) is that, while “ordered” collections offer a clean UI to re-order, “unordered” collections offer only a clumsy way to do so.
It seems to me it would be simpler and clearer to make all collections re-orderable, and maybe to order them “by added datetime” by default — this would unify the experience, and the user would not have to decide on an ordering mode, but only on the order. The real choice would then be the default presentation (by list or grid).
Ordering would still be optional, and, on collections where the order does not matter much, I would move notebooks only when I see that the current order is “wrong”. Most of the time it’s when I add a notebook to several collections, and see that it appears at the top of each, making the page that lists the collections boooooring. In terms of UX it would also be nice: the action would be made at the same place where I see that the order is “wrong”. (It would also be lovely to be allowed to re-order collections.)
I have of course no idea of the feasibility server-side.