And I would definitely call it "bending over backwards" to have Nature "invent" nanotubes to replace spider silk.

Peter being so smart helps his character because it shows that intelligence alone doesn't mean you will be happy and successful all the time.  Roger Stern once remarked to me that people think of Peter Parker as the "regular guy with powers" but he's not.  Peter is the "really really smart kid".  Peter's intelligence made him an outcast before he got his powers. As JB says above, being Spider-Man helps him deal with his social status.  But the problems in his life were already there.

AF 15 shows how badly Peter sometimes deals with things.  He's a genius,  He's not perfect.

However, I have stopped making this point in the past few years, as it has slowly dawned on me that a 29 year old who still screws up the same way he did when he was a teenager is indeed a loser.

Stan Lee & co. created their characters as complete people. If Steve Rogers had been bitten by the irradiated spider and Peter Parker had been injected with the Super Soldier serum, we would not have the same superheroes. Peter's youth, intelligence, family situation, social status, etc., these are all fundamental to whom Spider-Man is.

About the original teenage Peter, although he was harried in school, mostly by Flash Thompson, he was far from a loser -- particularly with the girls!

Parker was a loser with the ladies in much the same way Chandler Bing was. "Oh, you poor devil! You have to sleep with a different beautiful woman every week!!!"

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And yet Chandler had a better paying job, which could mean more opportunities to impress the ladies...

I saw an interview with him somewhere (can't find it here) that chalked it up
to a production/filming issue -- he just couldn't explain why those bulky
webshooters disappeared under a skin-tight costume

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SER: Uhmm... because they did?

It's sort of like the bulky Batman costume in the recent movies. OK, fine, the costume is designed so as to be bullet resistant and knife proof... but it's not real, it doesn't have to actually do this. Christian Bale isn't going to have to *really* fight crime, so there was never a real reason why the costume couldn't look the way it looked in the comics (and even in the comics, they've made a point of saying that the costume is bullet resistant while still looking the same for the most part as it always had).

I do agree that the second movie demonstrated Peters intelligence better...

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I guess so if I have to bare Parker talking about faux science with Octavius, then later after knowing his powers is faulty he decides to web swing through the city with hazzardous results.  I must mentioned Parker does this several times which generated laughs.  Did he really demonstate his intelligence just because he sparked a conversation with the villain?  Movies are a visual medium, and having a chit chat about smart stuff doesn't equate him being intelligent while doing stupid things through out the film.