Back when he first bought the Cowboys, he did some unthinkable things. First, he fired Tom Landry, who was the face of the Cowboys since it's inception, and brought in Jimmy Johnson. Team went 1-15 in Johnson's first year, but to his credit, Jones kept him. Three years later, the Cowboys win their first Super Bowl since the 1977 season. That Cowboys team had so much talent, it should have won five Super Bowls in a row. But that's when Jones started to lose his edge, letting Jimmy Johnson walk, then replacing him with unorthodox choices like Switzer, Gailey, Phillips. Even Bill Parcells couldn't turn the team around the way he did with the Giants, Patriots, and Jets. Now, Jerry Jones is noticed more for his fucked up plastic surgery than he is for running a franchise that hasn't won since 1995.
I don't think Jerry Jones ever had an edge. That whole Dynasty came about from Minnesota giving away their future for Herschel Walker in order to go for a Super Bowl.