I always thought the web shooters were a redundant addition to Spider-Man's power set. You don't need him to be inventing fantastical devices like he's Reed Richards to convey that he's a smart kid. Besides, what has Peter done with his engineering/chemical knowledge since then? Pretty much zilch, and it's rarely touched upon by writers. Why didn't he sell his "spider silk" invention for millions of dollars? For such a smart kid, he's pretty dumb. Raimi circumvents all that by simply making the web shooters organic.