It's worth noting that the current Norman doesn't remember that Peter Parker is Spider-man. He wouldn't even remember why he targeted Gwen--"Hey! I screwed that chick once, right?" Also, Warren Ellis' Norman is pre-I-forgot-everything Norman. Remember they stopped fighting to watch Peter's televised coming out.
The Deadpool series has canon that says Norman intercepted information on how to kill Skrull Queens that Fury had sent Deadpool to get. That Norman deliberately used that info to kill Skrull Spiderwoman (which is confusing, because haven't other skrulls died from being shot? Jarvis Skrull ferinstance?).
Madgoblin isn't always right but he is definitely right that Norman works better as the monster that no one else can see.