I think one simple change that would have stopped the latest Labour psycho-drama is to put in place a rule that if you change PM you immediately call a general election. I reckon a lot of MPs would be a lot less keen on regime change if they had to put their own seat at risk.
Yes, there are times when your PM is so disastrous, so corrupt, so unfit to serve that you simply have to get them out immediately, but chopping and changing just because they are down in the polls is fucking stupid. Especially when (in Burnham's case) you have a desire for power and see this as a quick route to get to the top.
On Starmer, I think he is honest and competent, which are (for me) the two most important characteristics in a PM. I don't want a charismatic, exciting PM in the same way I don't want an exciting pilot when flying to the US. I want the flight to be as boring as possible, not some showman who chucks in the occasional barrel roll for funsies.
The UK was clearly steadily improving on his watch. Economy was growing despite Trump's best efforts, NHS waiting lists were going down, immigration (if you happen to have replaced your entire personality with "genuine concern" over small boats) has dropped massively, and all the Tories could say in response was "We would have made all these numbers bigger/smaller." despite 14 years of evidence to the contrary.
I reckon if Starmer had been left to serve out his term, we'd be in pretty good shape and looking at a return to a (probably slightly smaller) Labour majority in the next GE.
As it is, Burnham will have maybe a month's grace before everyone is asking Magic Andy where their sunlit uplands are.