I agree with you on that. To clarify, when I used the word "archetype" I was talking only about the superhero aspect of the character; that is, the superhero's abilities and motive. I think those two character aspects are what set superhero fiction apart from other genres of fiction. If you look at the overall character, "archetype" takes on a different aspect I think; in the overall sense, Batman would fall into the "creature of the night" archetype.
I'm also wondering about how to categorize Spider-Man.
For powers, I'd say he's an example of the "Accidental Hero": someone who gets his powers from an accident of some kind. Daredevil, The Flash, and The Hulk are other examples of this.
For motive, it's harder to say; perhaps a mixture of guilt and Purity of Heart. There are other "guilty" superheroes out there, who became heroes to atone for past misdeeds; Plastic Man is one. The "Pure of Heart" superheroes are numerous; Superman and Captain America are the two prime examples.
For overall character, Spider-Man is a Wish-Fulfillment character: the wimpy kid with secret superpowers. He's not really the first such superhero... Captain Marvel (the Shazam! one) falls into that category too.
All of the above is just my opinion, of course! :)