A very good question and there really is no answer. You need lady luck and it was lady luck that happened when HHH was punished for the curtain call and Austin was given the ball to run.
Austin didn't really get that much of a push from his King of the Ring win. The next PPV (In Your House: International Incident) I believe was a rematch with "Wildman" Marc Mero, a midcard deal. The main event was a six man tag match: Camp Cornette (Vader, British Bulldog, and Owen Hart vs. Shawn Michaels-WWF Champ, Ahmed Johnson-IC Champ, and Sid, replacing a suspended/fired Ultimate Warrior).
At SummerSlam, Austin didn't even make the PPV. He had a "Free-for-All" match against Yokozuna, where Austin got beat up most of the match. He won after the rope snapped as Yoko went for the Banzai drop. Yoko crashed and landed like a beached whale and Austin got the pin.
He had a few more matches with Jake "The Snake" Roberts. I remember when they had WWF Livewire and fans could call or send e-mail (via AOL.com) to ask their favorite wrestlers questions. One guy called and asked Austin why he didn't have a title if he was so great. Austin retorted that he didn't have a championship because everyone with a belt was scared to face him. He cited his repeated wins over Marc Mero yet lamented that he never got a match with Mero, after Mero won the IC title. An e-mailer asked why Austin hadn't received a WWF title shot, especially since the previous KOR winners got title matches, particularly at SummerSlam (O.Hart-'94 and Mabel-'95).
Austin was supposed to face Savio Vega yet again at In Your House: Buried Alive. Mero was supposed to defend the IC title against Faarooq; but Ahmed Johnson beat up Faarooq with a 2x4 before the match, resulting in Goldust getting the shot. Michaels didn't even fight at that PPV. So, Austin got no title shot at all.
Hunter Hearst Helmsley subbed for Vega, due to an injury to Vega. Austin beat Helmsley at the PPV; the next night, Helmsley beat Mero for the IC title (courtesy of the "Perfect Hoax").
Austin's star didn't really rise until he faced Bret Hart. To me, that had more to do with their personalities and styles. By that time, Austin's King of the Ring win had all but faded in relevance.