If Another Pilot Had Been Chosen, How Would Things Have Been Different?
Had this TIE jockey not lost his mind, or had an actual competent pilot been chosen, Darth would have placed his next shot right up Luke's colon. He had it all lined up in his Pong-quality targeting system.
No, Han Solo wouldn't have had time to stop him--again, he'd already wasted his one strafing run on Vader's nameless escort rather than Vader himself. Luke would have died in flaming chunks, just like all of his fellow pilots, and would never have gotten a chance to fire the torpedoes into the Death Star's air conditioning vent.
The Death Star then would have rounded Yavin and blown up the rebel base. Were there other rebel bases? Presumably, but this one had the entire upper echelon of the Rebellion in it, including the Princess herself.
"Somebody get that goddamned robot out of here."
All of the people who would eventually lead the movement to bring down the Empire a few movies later--including Luke and Leia--would have died. And how long would the other Rebel bases have lasted? The Death Star would have been free to do what it was designed to do: roam around the galaxy blowing up unruly planets.
Wait, couldn't one of those other groups of Rebels just staged a similar attack, maybe have some other farm boy fire torpedoes into the same vulnerable spot? Almost certainly not. Having survived the attack, the very first move on the Empire's part would have been to figure out just what exactly the Rebels were trying to do when they attacked the trenches with their tiny ships. "Oh, right, the shaft. We need to fix that before next time."
"Tell them to throw a grate on there."
Remember, the only reason the second Death Star in Return of the Jedi had the same vulnerability was because it was half-finished, its guts open to the world. Not so with this one. They'd have been free to retrofit it with one of those fancy shield generators like in Jedi only, you know, one that's actually on board the Death Star and not located off-site on a moon full of Care Bears. Clearly the Rebels couldn't penetrate such a shield, since they wouldn't even start the attack in the third film before it was taken down.
But just in general, surviving the first assault would have taught the Empire some important lessons about surviving the next one. Specifically, that you need something more than those grossly inaccurate turrets and a hand full of TIE fighters to defend the thing. More invulnerable than ever, they would have started systematically blowing up any planets giving them even a hint of trouble. Like, say, Tatooine, or Dagoba, or Hoth. Remember, these people blew up Alderaan out of spite.
None of that happened, thanks to one nameless TIE fighter pilot with a habit of yanking randomly on his control stick at the sound of loud noises. So somewhere up on that stage at the end, when they honored basically everybody (including the damned repair droid)...
...there should have been a framed picture and a plaque commemorating this guy:
None of those people would be alive without him.