Andy Burnham unfortunately appears to have been unlucky with timing. Not enough known about him in 2010, too much association with previous leaderships by 2015. His political gravitas has been greatly increased as Mayor of Manchester and being 'King of the North', but unfortunately that also means he's no longer an MP.
He’s out of national politics and even this week made it plain he see’s Greater Manchester as a 10 or 15 year project, not wanting to be an MP for now.
Imho he’ll be the LP leader one day when he’s it’s opportune i.e not in the cycle when Labour are getting destroyed by the media and social media.