Longstreet suceeded at Chickamauga because a Union brigade was was pulled from the center of their line by mistake leaving a gap for him to plunge into. That had nothing to do with any brilliance on his part. The Yanks made a mistake and he took advantage of it. Don't get me wrong, I think Longstreet was an excellent general. What does that have to do with being president and developing an overall strategy for the war? Besides, Davis didn't didn't plan that strategy by himself. Lee was his top advisor before he took over the army in Virginia.
Okay, so Longstreet caught them maneuvering, I've been there, and I've walked through the gap -- it wasn't that big a gap. But you're right, he moved at just the right time. Just as Strong Vincent summoned help to Little Round Top just in time on the Second Day, and John Buford arrived on the western slope of Seminary Ridge just in time on the First Day of Gettysburg.
Bottom line, Rosecrans was an idiot, and he got creamed -- moving his line around in the face of the enemy, even when a general engagement had been in progress on his left since early in the morning.
My point is that Longstreet was there -- and that his being there was half the battle, and proof of his strategic ability. Polk, Bragg, and the rest of them brought with them an army and a willingness to fight, but not much else, as the returns from the battlefield showed. Longstreet brought a corps and winning ideas, and his maneuvers -- both strategic and operational -- set the Union generals back seven or eight months with a one-day effort.
My point is that a lot more of that kind of thinking would have made the Civil War a lot rougher for the Union, and it was already "plumb rough" as it was. Longstreet demonstrated the ability to think in sweeping strategic terms that the political and doctrinal strictures imposed by Davis shackled and immured, except just that once.
Oh, and by the way -- I've read somewhere that Longstreet advocated the Chickamauga action earlier in the year. It was his contribution to the discussion of the 1863 campaign, and it was turned down in favor of Lee's idea. Lee invaded the North twice, I think to menace the merchants of the Middle Atlantic states, but I'm not sure what his real objective was -- given that he'd have a Union army twice his size between him and home at all times, if the Union commander were halfway intelligent.
In any case, Longstreet's ideas were shot down, and Lee's proposals were approved, and the rest, as they say, is history.