It is easy to be borne down by the sheer familiarity of this temptation story, or rather of the story we may well have constructed in memory from the traces of three stories (or maybe more), rather than attending to the text itself.
Matthew’s temptation story is distinctive in a few ways. First and foremost, he separates the forty day fast from the temptation itself. Rather than being the means or the medium of temptation, Matthew implies the fast is first and separate, a time of deliberate preparation. Jesus is not yet in the arena, but in hard training for what will come.
Second, when the temptation begins, Matthew, like Luke, expands on the bare Markan reference to Jesus being tempted, depicting the classic threefold game of proof-texting with Satan that we know well. Both Matthew and Luke have the tempter begin with the stones-into-bread gambit, taking up the fact of the fast and the resultant hunger, but Matthew then moves through the testing-behavior instance (“throw yourself down”), to reach a climactic moment - the fitting one, I think (sorry Luke) - where the worship of Satan is offered as the price of receiving all the kingdoms of the world (whereas Luke reverses the second two).
The “worship” sought here - and generally in the NT - doesn’t mean liturgy, or for that matter the manufactured ecstasy referred to as “worship” connected to musical performance. It just means obedience and service. The one ritual performance associated with it - here, but also at some other key disclosive moments through Matthew’s Gospel, first at the beginning with the Magi and then at the end with disciples witnessing the risen Christ - is prostration, the fully-embodied demonstration of that service. The false form of worship sought here is allegiance, with obedience in the political realm presumed above all.
Above I said we might construct our temptation narrative from three “or maybe more” stories, thinking of the ways the figure of Satan is treated so differently across biblical texts, others of which might crowd into our minds when reading this one, themselves demanding our obedience and attention. Although this character is called “the devil” in the introduction (v. 1), and even though “tempting” is quite often attributed to the devil or Satan otherwise, Matthew’s temptation story is the only time in the Gospels that “the tempter” is clearly the preferred name for the character (cf. 1 Thess 3:5).
While there is no question of the evil and insidious nature of “the tempter,” there is nevertheless a sense (underscored by use of this title) that he is performing a task that falls within the scope of the divine plan. All the versions of this story connect this wilderness experience with the leading of the Spirit, after all; Matthew is quite explicit that this temptation is the reason Jesus was “led up” there by the Spirit, even though the fast comes in between. So this process and the role of Satan are still reminiscent of the picture in Job (see chapters 1-2), where Satan is the agent of evil, yet works within the larger ambit of God’s plan. This is quite different from ideas of Satan as the sort of anti-God, source and embodiment of cosmic evil - maybe the Satan of the apocalyptic literature, and more so of medieval cosmology and piety, as well as of some fundamentalist silliness.
The danger of this Matthean tempter, the really insidious nature of his threat, is how moderate and reasonable he is. How appropriate for him to quote Scripture, rather than to spew filth; how much more dangerous to offer bread than luxury; how fitting to offer Jesus the end of his labors - reign over the earth - without the path he must tread to obtain it. The proposed misuse of power gives off only the faintest of odors, but threatens to cause all to rot.
Much of the sniffing around for traces of metaphysical evil that has become strikingly normal in some parts of the Church in the last few decades - claims about what amount to vibes, much of the time - seems to swallow camels concerning misuse of power, of things, and of people, while straining at various gnats of odd feelings. Evil is more likely to be banal, or even straightforwardly appealing to common sense, than to really make the hairs on the back of your neck stand on end. And yes, it often quotes scripture.