1) Method Using fictions as a method can be helpful I think, and for this reason I would mention the book of Han Vaihinger https://en.m.wikipedia.org/wiki/The_Philosophy_of_%27As_if%27 It is better to actually read Vaihinger's book if that is possible because the Wikipedia article is not too good. I often use my highly ideosyncratic Hegel, my very own Hegel, as a method to come to grips with the world; not as the absolute truth, but as a method. So I would probably put your comment regarding Stewart and Trait under the category of Method.
2) Time
Both the play or drama and life are time limited, so the temptation to make an idol or fetish to solve our problems is very real. This would not be mere Method, but it would be Ontology.
On the other hand, the full story, without the device of the Deus ex Machina, would be the repair of the world, but this takes time. More than one lifetime. Can the repair of the world ever be completed? If it were finished it would not be an idol because there would be no need of an idol, it would just be a better world. I don't know the answer to the question of whether the repair could be completed, but I feel certain that there is a lot written on this subject.
It was Karl Marx I believe who specifically recognized that man is quick to solve his problems with a fetish or idol. Why? Probably because we can't resist having an ersatz answer to life's problems within our single lifespan. This was Marx's concept of reification. If Marx did not discover reification, he certainly developed it with extraordinary genius.
So we know that if we think of an orange as just an orange, we have a fetish or idol. But no, the orange came from a seed, it was planted, tended by humans, nourished by nature, transported to the market again by human beings; so there is a lot of history wrapped up into "this single orange", this idol, this fetish, this ontology.
Now say, for instance in the Kabbalah, is Kether ever reified? No. I don't think so, and this is very wise I think. It is hidden and resistant to man's shortcuts, ontologies and so on.
To move this back into "purely" philosophical discourse, we probably come, at the end of the day, to something like Hans Gadamer, "Truth and Method", just as one example. Broadly speaking, hermeneutics, which is never finished until we are finished! But tradition as a topic is a bigger topic than hermeneutics itself. In other words, what is taught in the universities today is often a reduced hermeneutics.