Here's the thing for me.
I think the spider bite is cooler if it just puts Peter at his physical peak while unlocking bits of his brain or physiology that allow him to operate electromagnetic waves to stick to walls.
There's a bit of sci-fi bullshit in there but the long and short of it is I don't like the idea that Peter grew new organs from the spider bite, I think he should still just be a regular guy on the inside.