Yes, but then he would've been Iron Man instead of Spiderman. And Tony Stark would have to think of some other superhero to become, and still be able to build an iron lung into his costume. And if Peter Parker had all those other spider powers besides web-spinning, he would've simply been hogging good superhero ideas by becoming Iron Man, too.
See how clear things become when you apply simple logic.
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Legend, oh legend, the third wheel legend...always in the way.