Yes:
Let's say, you want to generate forms from your JSON Schema. That's a pretty good use case, because the JSON Schema already contains a lot of information to do that. You'd want to add some additonal properties that are form-generation-related, of course.
It is crucial (for UX) that the form inputs will be rendered in the order you've specified and that the form remains in that order (and is not randomly shuffled).
Once you've submitted the form the resulting data may be unsorted again, it dosen't matter. If the order is of matter after submitting the data, an array would definately be the only right data format and using an object a mistake in choice of data structures. In that case the use of "properties" would be wrong in the first place, "items" needs to be used instead.
For Validation of the resulting Data, the property order doesn't matter as you see. As you pointed out, an object structure is much nicer to work with in this case. But for the creating of the form, the property order it is still mandatory.
So using the propertyOrder for validating the order of properties is probably not a good idea, since the data structure itself does not guarantuee that order. It simply is the wrong choice, though in many cases that choice has been made because current JavaScript VM's are "nice" and preserving the order up to a certain size of the object. (But they would not have to, and once you exceed that size your whole program would fall apart if it depends on that order)
This makes the case a bit tricky. If you think it in data structures, the properties attribute is a Collection (that will be serialized to an array)
I hope that'll make it a bit more clear?
Best,
Simon