If Jesus and Satan (the latter in spirit or within a host-body) began traveling from some transjordanian wild spot towards Jerusalem, the most natural senic bypass (of significant altitude) would most likely have been Mount Nebo - which certainly has some impressive vistas, but I'm pretty sure they stop short of Abilene, let alone the oikoumene, let alone the kosmos. For that matter, no mountain in Palestine (or on Earth) would be "very high" enough to serve much better.
Thus, wherever they went, if they went, it wasn't height that produced whatever Jesus saw.
Therefore, logically, IF this event is historical, THEN Satan must have shown Jesus a vision in his mind's eye. That's not too far afield from what Matthew and Luke give us toward angel-ology. For instance, we've already discussed the likelihood of non-audible talking, aka telepathy, as perhaps also with Gabriel to Zechariah & Mary. More importantly, Matthew says angels spoke directly into Joseph's mind through his dreams. So, apparently, Satan offered Jesus some sort of visual download, and Jesus accepted the imaging transfer. All plausible enough, as I say, so far as we know.
Anyway, the situation is either fictitious OR ELSE we have to conclude Satan somehow gave Jesus a vision. Fine, you say. Fair enough maybe. But that still doesn't explain Matthew's insistence about this "very high" mountain!
Right. Now we come to the rub.
A skeptic might say that it looks like Matthew expected his readers to take the direct implication quite literally, and therefore Matthew himself must have had an unrealistic view of his own purported event, which makes it impossible, and thus fictitious. A liberal believer might say Matthew intended the story to be taken as fiction. An evangelical apologist might defend Matthew's text on some technicality, and then shift the conversation as quickly as possible toward Luke's version of this same event. But now _I_ find myself looking for _my_ way of looking at these sorts of things. And so, what do I think?
I suspect Matthew himself was a little unclear on the precise geography or mysterious mystical aspects of what might have been going on here. I think Matthew had heard the original story from Jesus himself, but probably not all the details. In other words, I assume Matthew mentioned the mountain because the vision had actually happened up on some mountain, but I suspect "very high" was a phrase that had grown up over time in retelling the story. I think "very high" just made people more comfortable accepting the story.
I honestly think most first century common folks were at least smart enough to understand that you can't see the whole earth from a mountaintop, but at the same time I think many of those same folks found the setting more suitable, and found the incredible vision more credible, after hearing it had been experienced from "very high" up a mountain.
Now, skeptics point out that Biblical stories often show holy men finding God up on mountains, and skeptics claim this parallels things like Olympus in Greece - that a primitive mind finds it easier to imagine God touching Earth where it's still nearer to Heaven. I agree with all of that, actually. Skeptics, however, go on to conclude that such primitive leanings mean all such stories were probably made up. I don't agree with that in the least.
Yes, of course, primitive people must have found it easier to envision divine activity taking place up on mountaintops, but that hardly means all such stories are false, or should even be suspect. To the contrary, the simplistic nature of this convention might only (merely) help to explain why such stories were more popular with everyone - and perhaps more quickly accepted as credible with the simplest of folk.
So, how and where did Satan tempt Jesus by showing him all the kingdoms of Earth? On a mountain, with a vision. In my humble opinion, Matthew's style of presenting the story does not make its basic claims any less credible.
Next: Matthew vs. Luke - Sequencing Jesus' Temptations