Except, of course, that one of the most popular superheroes ever has the proportional abilities of a spider! And before him, there were heroes called the Fly and the Tarantula. Irony? Or do the animal's powers trump any squeamish considerations? Spiders have a fun bag of tricks, and once you're contemplating using the spider as a totem animal, you can follow through and make him a bit creepy to the in-universe public.
Many animal heroes (not to be confused with hero animals, we'll do super-pets later if you like) don't have any powers at all, but chose their animal as an emblem, taking on its perceived qualities if not abilities. Batman is the most prominent example, and like spiders, bats don't exactly have the best of reputations. Batman deliberately uses the his totem's ickiness to strike fear into criminals, taking his cue from vampires and pulp hero the Black Bat. The Black Panther is regal and a fierce fighter. The Black Widow is a femme fatale. Slinky cat burglars naturally prefer the cat as their emblem. And some heroes, like the Ted Kord Blue Beetle and the Tick just pick something and make it work for them. One way or another, our understanding of these heroes is filtered through our understanding of the animals they've chosen. Most children are fascinated by the animal kingdom, will be drawn to these characters without much prompting, and may even invent their own heroes based on a selection of Safari cards they have on hand (it's not just me, is it?). Yes, it does mean we get bottom-of-the-barrel concepts like the Kangaroo, but that's still memorable!
What would be YOUR totem animal?