I can see the political benefits of recruiting Alan Milburn as a policy czar, but in terms of good government what is the point? In his most prominent position in the last government, as health secretary, he didn't achieve anything of note other than in spending more money. Maybe it wasn't his fault, he was reputed to have tried to implement reforms, but even so he left without any major accomplishment to his name.
He supposedly had an important role in advising the Australian Labor Party in their last landslide election victory although even his skills as a political strategist must be called into question when you consider that as the UK Labour Party's election supremo in 2005 he had to be rescued by Gordon Brown (remember when Gordon Brown was popular!?).
So why is he being entrusted to devise the government's policy on social mobility? Being broad minded enough to consult policy experts regardless of party affiliation, and few people would object to an acknowledged expert advcising the government even if he was a member of the Labour Party, Frank Field is exactly the right person to appoint to advise on welfare reform for example. The only reasons that I can think of for appointing Alan Milburn though are to embarrass the Labour Party and provide political cover for the Coalition.