I wasn’t in favour of the decision to appoint Mandelson. Can’t speak for others.
I believe Burnham would have won the by-election. Polling suggested he would. Not all 4/9 chances win but that was the price Labour were with the bookmakers when it was believed he would be the candidate. It would certainly have been a much closer outcome if he had stood, rather than the somewhat anonymous candidate that did.
“Obelisk” in Slugger, a long time poster on that site, clearly thinks he would have won as well.