Why blogs are great - more media exposure
The reason blogs are so great is they provide an opportunity to put forward your point of view, especially if, say, the BBC write something that's not entirely true.
I don't so much believe Alan Milburn isn't "pulling his weight", rather there's no evidence to the contrary, avaialble for a constituent (I am a constituent) to see. If Alan Milburn had his own blog, what he was doing would be available for all his constituents so see.
Just like the Tim Yeo blog mentioned in the article, this blog will be handed over to Mr Milburn should he ask for it. Unlike the person running that blog, I'd even show Mr Milburn (or his staff, though that's not really in the spirit of blogging) how to run it, and help them convert it to a more 'Labour-themed' style.