I'm still convinced Skye's actually a.k.a. Jessica Jones, and the Jessica Jones show spins off of this.
Basically she would eventually have a knack for working under multiple ALIAS's after going undercover, has no real identity anymore, and can offer the save services as Shield with her own private investigation firm.
It's true she does have a background that matches Spiderwoman/Jessica Drew. But there are actually quite a few similarities between Skye and Jessica Jones..
While working undercover they discover Skye is getting better at what May hates...working under assumed identities and false personas...
In other words: acting. Sort of like how Black Widow had to act in IM2, and got rid of her accent. BlackWidow is a very talented actor, can drop and change accents, knows multiple languages, can fake it effectively, sorta like Trevor...
Skye sucked at pretending to be May.
However, Simmons and May really suck at "acting" undercover.
She's been launching her own private investigation into her parents this whole time. Coulson hinted in one episode that she has a talent for reading people, and that one day she might be able to assess people for shield's Asset Index thingy. Whatever it was that Coulson said at the end of that episode, she said it was a "bad name".
Maybe she can come up with a better one, or shorten the name Coulson listed off and change it to A.L.I.A.S.