Normal Staraptor can hit te with Close Combat, bit the thing is, with Reckless and STAB, Flare Blits could be unstoppable. I think Staraptor (And Swellow) are one of the few who appreciate their Normal typing and only for STAB Double Edge/Facade.Of course Normal is always outclassed, but it's still not that bad (although Fighting / Flying Braviary would be awesome). A Fire-Flying Staraptor gains coverage on Steel, but lose to Rotom-W and even M-Scizor still takes a lot from Scarfed Brave Bird. Sure, you beat Aegislash, M-Mawile, Ferrothorn and Skarmory, but that's a trade-off I can accept, given how annoying Rotom can be. And Normal brings you a reliable STAB with no recoil, which is nice.
And with SR on, it's definitely going to kill itself even faster. I think that a Flare Blitz on Rocky Helmet Ferrothorn kills you.
I agree Normal is not great, but it still provides a niche to Staraptor. I'm unsure whether he would get it if he was something else (except Fighting).
Normal is a good type offensively and not a bad type offensively. Normal flying gets neutral damage from fighting but it can't appreciate other stabs. Noctowl could be a slightly better Pokemon if it was Normal Psychic for example.