Part I: It Wasn't a Story, It Was a Writer's Quirk
The totem story wasn't a bad idea necessarily, but based on the execution it was probably never going to be a significant or lasting addition to the Spider-Man premise or the serial narrative. At a fundamental level, it simply had much less going on than there appeared to be on the surface. As I'll show at tedious length, the totem storyline falls apart thematically and at the plot level when even a few very basic, simple questions are asked. In the end, it wasn't an idea or a perspective; it was a hollow exercise in yammering vaguely about the words "totem" and "animal."
I'll start with a cheerfully unfair comparison. Probably the most memorable example of adding a spiritual or mystical component to a superhuman origin that had previously been "scientific" is Alan Moore's Swamp Thing. Now, that's an unfair comparison, since Moore had both a freer hand and a larger goal when he revised Swampy's backstory, but it's undeniably the touchstone for this sort of thing. Moore revised Swamp Thing's origin to fundamentally change the stakes of the book. The plots shifted radically. Instead of being Alec Holland's quest to regain his humanity, the story was now about Swamp Thing's quest to come to terms with his lack of humanity, and to discover what he really was and what powers and responsibilities -- eh? eh? -- his new state of being entailed.
More basically, however, the reason it worked, and indeed, gained lasting acclaim, was that it changed the themes of the book as well. Swamp Thing became, more or less permanently thereafter, a title about a very specific, increasingly detailed mystical cosmology of elemental forces and avatars, heavens and hells, of ecological parables and tales of the difference between nature's perspective and humanity's -- and most of all about the practical actions needed to retain the balance of these forces and perspectives. That was clear from the very first arc, where the villainous Floronic Man becomes the vengeful self-declared avatar of the plant world, slaughtering human beings for polluting and deforesting and so on...until Swamp Thing pointed out the very real ecological role of all the "meat" the Floronic Man wanted to eradicate, at which point the poor villain lost his connection to the plant world and went irretrievable, solipsistically mad.
Put briefly, Moore had a vision, and made his changes to spell that vision out, to set an agenda and follow it through.
When we compare the Spider-totem, the whole thing seems much less ambitious and, more damningly, much less considered as a a storyline.
Superficially, it didn't start from the same place Moore's revision did. JMS doesn't really explore deep spiritual visions when he develops superhero origin stories. Rather, he simply likes to rewrite "random" origin events into intelligently directed, even destined occurrences. In his run of Fantastic Four, he explained that the cosmic rays storm that had empowered the heroes was actually the work of a member of a heretofore unseen intelligent alien race; in his own Rising Stars, superpowers are dynastic and predictable inheritances, not the results of mischance or accident.
It's less a theme in his work than a preference, though. He doesn't seem to think of predestination or spirituality or intelligent design as actual themes with implications and importance in any of the works listed, for example. Rather, in his comics work he seems to be one of those writers who seems to dislike coincidence as the basis of fundamental, premise-making plot points.
The problem in a shared-universe feature work is that he rarely follows through on the reasonable implications of the plot changes of this sort of premise revision. In Fantastic Four, for example, we're left to wonder where the cosmic rays that created the Red Ghost and his Apes, the U-Foes, and so forth came from. As written, the event that empowered the heroes should have been singular and unrepeatable. The JMS story sort of forgets those other cosmic-ray characters and their origin stories exist, which is part of why it's never been referenced again.
The other reason the story has been mostly forgotten is that the new aliens that JMS tied to the origin retcon weren't very interesting, and once they stopped showing up, no one ever needed to refer to what they allegedly did again. As you'll see, that's essentially what happened to the totem storyline as well -- the consequences were so thin and so uninspired that even when it was recently brought back up in the storyline that -- ugh -- resurrected Kraven the Hunter, it was radically altered. That story even went to the trouble of assuring us that Ezekiel, the one character from the original totem storyline with a chance of catching on, was really dead and really not coming back.