It's interesting. Not long after Labour came to power there was some polling that suggested something like 75+ % of the population favoured some form of wealth taxes. I don't know how many things you could get three quarters of the UK population to agree on these days but I can't imagine it's too many. So arguably irrespective of the fact his majority is a function of the FPTP system he would probably have had some moral authority to do something in this area but he won't touch it with a bargepole.
I suspect if you sat down with Starmer and accused him of being much too timid he would shoot back that it wasn't in the manifesto and you can't just do things you haven't campaigned on. When you asked him why he didn't campaign on it rather than saying whether he believed in the idea or not, I think he'd argue that if that had been in the manifesto that would have been seized on by the press and they'd have been unelectable. Who knows whether that would have been true or not but one of the few things Tony Blair got right in his recent missive was that Labour got elected for simply not being the Conservatives and that was a deliberate campaign approach. That was enough to get him elected but not a basis for governing meaningfully in the times we are faced with.
So whether Starmer is simply a well meaning technocrat at a point in history when we don't need a technocrat, or a more knowing stooge, is all now academic. He wasn't the right man to grasp the nettle, and it is a nettle.
If Burnham wins the by-election and then succeeds in unseating him he potentially does have a chance to change the narrative and do something more radical. However at the point he tries that the press, reform and the conservatives as a minimum would be up in arms and demand an election on the basis he has no mandate. That's not his only problem, he needs to avoid spooking the markets whilst at the same time explaining to a frustrated, cynical and understandably impatient electorate that the changes required are going to take time to design and implement effectively. All the time against a backdrop of relentless attacks from the press that will make the treatment Starmer's had look quite tame.
In order to bat all that away imo he needs friends beyond even his supermajority in the house. Partly I think because the right of the party wont necessarily get behind him and partly for the moral authority it will confer. He's not going to have time before the next election to do a lot of structural stuff but I think as a minimum he needs to find an initiative or two that shows people he's actually serious. Imo he needs to reach out to the Greens and the Lib Dems and include them in the conversation and probably others too sooner rather than later. The next election could well be the battle for Britain's soul. I doubt even with a reset Labour can win that on its own. Whether Burnham is the person to unite enough allies to win the day overall we'll have to see.