I don't think pairing her up with Spider-man, either as an ambiguously romantic interest or as a simple recurring platonic friends character, really brings anything to Natasha but another place to cameo. And she has plenty of places to cameo already— Avengers, Iron Man, Captain America, Wolverine, that's most of Marvel's A-list franchises already, plus her long history in Daredevil. I don't see how learning to respect Spider-man's abilities is a compelling arc for her character, since I really doubt she honestly disrespects him anyway. And, again, there are plenty of characters Natasha already has a more intimate, personal connection with, it's not as though we never get to see that side of her. Meanwhile, I can't imagine Peter would care overmuch about becoming friends with her? He has a rich and expansive supporting cast already, and established relationships with Ms. Marvel and Silver Sable that are getting some play, now. I don't see what Natasha would bring that pre-established relationships don't, I suppose.