Really like your anology, mind if I use it?An analogy we like to use around my group of RL friends...
If N were superpowers that represented how the mind goes from point A to point B, Ne would be super speed and Ni would be teleportation. Ne is clearly faster than Ni, and yet Ni often gets there first. Ne can move through patterns at blazing speeds narrowing down possibilities until it gets where it needs to go. Ni percolates until it is ready to have an aha moment, and then it just does.
If Ne and Ni were having a race from the United States to an address in Japan, Ne would be like the Flash, running in the general direction toward Japan, using rapid succession of trial and error until it found the address in what would seem like the blink of an eye... only to find Ni already there. When Ne asks who it got there, Ni has no answer other than it simply did. Meanwhile, Ne can give a detailed account of its course, recounting how it ran a few thousand circles around Ni before the race started. Ni was in one place unmoving as it summoned up the power to make the shift, and then it was suddenly in the right place with little or no recollection of the distance in between.
I would frequently make my ENTP buddy insane with my inability to explain how I was consistently coming to answers before he could. It made no sense to him because it was so clear that his thinking speed was about ten times mine (I'd wager more than that actually). But, while he was busy with his explosion of possibilities that erupted from any one source, I was scanning the entirety for the one answer.