Alford left because he wasn't gonna have a legit shot to promote into a coordinator role at ND. He was passed up in 2011 when they went with Chuck Martin to replace Molnar. He was passed up again in 2014 when they replaced Martin with Denbrock. He was passed up AGAIN in 2015, when they brought in Sanford to be the OC.
Obviously, working with Urban Meyer was definitely a tempting opportunity, and perhaps he saw a better shot to promote or work his way into an OC role elsewhere at Ohio State working for one of the top offensive minds at the time. Didn't work out that way.
May be the same logic for his move from Ohio State to Michigan, where he's chasing a potential promotion. I just think he's a lifetime position coach.