It wouldn't be unreasonable for Starmer to have said to Streeting: 'Ok, I see your position but you need to challenge me officially. Gather your support and do that.'
Because that would be proper, unlike the parade of briefings, performance resignations and unelected body interference (unions) that's going on now.
But those in previously Labour areas now voting Reform will not be changing their views because Starmer is replaced by Wes Streeting. Streeting is no solution in the outside world, only in the inner bubble.
Labour have a romantic fondness for the leaders they never had and Andy Burnham is their current Prince Over the Water. But in the outside world he's just another Labour bloke who's been around for ages and is quite well-liked as a mayor. Mayors are very different figures to prime ministers - Boris Johnson was a popular mayor.
Burnham - who should be discouraging his supporters from calling him 'King of the North' because no-one else would call him that - has lots to lose. He's rather insulting the people of Manchester by openly considering binning them off mid-term for a better personal opportunity, and to be an MP he'd have to be gifted an artificially-induced by-election and constituents aren't usually keen on their representatives bailing out and telling them to vote for someone else approved by the Party. They could get very Boaty McBoatface about that. Princes always look more attractive when they're still over the water.
The Labour party are failing because they aren't a party with an agreed purpose and they can't represent enough of the country - it would / will be hard enough for a focused and united party to represent fragmenting Britain but Labour are fundamentally riven by the uneasy alliance of ordinary and poorer working people, a comfy middle-class 'liberal left' and hard ideological socialists that have always been pulling it apart.