Excellent post... let's go one step further for the you can't just keep firing and hiring people, the carousel has to stop! crowd:
In 1987, Larry Smith was hired by USC to be their football coach. He wins a conference title or shares it each of his first 3 seasons. However, his last 3 years things spiral down, going 8-4, 3-8, then 6-5. They promptly fire him. In 1993 USC hired John Robinson, who quickly takes a team who went 6-5-1 the year prior to the top 25 the next year and ties them for a conference title. John Robinson his first 3 years, wins 8 games, 9 games, 9 games, sharing two conference titles. The wheels come off the next two years and he essentially goes .500 both his final two seasons. He gets fired. They then fire Paul Hackett who gets 3 seasons to basically not do anything with the program, and he is fired. Then to your point, they hire Pete Carroll, a failed NFL coach, and he takes them to the promised land.
You can't just stick with something and hope it works. Salaries now-a-days make things a bit trickier. But there's other teams just like USC that eventually get it figured out (Alabama, Oklahoma). There are so many coaches out there, and then ones you wouldn't even give a chance to, that could do wonders here. What if we hired a failed NFL coach like Pete Carroll, how mad would we be? There's countless other guys I could point to that weren't great that went on to be successful elsewhere, but the point is there's options.