He didn't at Michigan State.
It doesn't matter how good you are, there are ceilings at most programs. Saban won national championships at LSU and Alabama because of 1) the inherent resources available at those schools; and 2) his ability to get the most out of the talent available to him. In that order.
If he went to Baylor, he'd win a bunch of games. He would not beat Texas, Nebraska and Oklahoma, let alone the next tier of Big 12 teams, with enough consistency to contend for a national championship.
No, he didn't win double-digit games at Duke. His best record in a single season was 8-4 in 1989, when he won a share of the ACC title and got his butt kicked by Texas Tech in a bowl. To give you an idea of how good Duke actually was, they played one of the teams that shared the SEC title in 1989. Tennessee clobbered them 28-6.
The best teams in the 1989 version of the ACC, other than Duke, were Clemson, Virginia and NC State. Virginia was the only one of them who was really any good (the same team we beat in the Sugar Bowl, a year later), and they beat Duke head to head. Everybody else was either young, or really bad.
If he had stayed at Duke in 1990, he would have his butt handed to him. That was the year Georgia Tech was national champions and UNC figured out how to play football under Mack Brown. Virginia was No. 1 for a month of the season, Clemson was better, and NC State and Maryland both made it to a bowl.
He would have left for a better job after 1989 even if Florida hadn't been open. We all knew he would. (I was already living here at the time.) Spurrier knew his window of opportunity at Duke was about to close.