The problem is that the British constitution, such as it is, and the conventions and practices which have risen up as a result essentially depend on the 'good chap' theory of government - the idea that ministers and civil servants recognise the limits of their power, self-regulate, and resign when they ought to, even without any mechanism to force them to. Keir Starmer will have learned this in the first year of his LLB and, I have absolutely no doubt, subscribes to those principles himself.
The 'good chap' theory unfortunately breaks down when public life becomes infested with charlatans. We saw this in the way that Westminster seemed totally unable to get a grip on Boris Johnson until his own MPs turned on him, and it has clearly broken down when vetting Peter Mandelson. The whole system - including any vetting - assumed Mandelson would put honour first and he clearly couldn't help himself, which at least shows he's consistent.
Sir Keir is like a mirror image of Johnson in this respect, shattered by the same fault line. I fundamentally believe he (Starmer!) is a decent and honourable man, and that of all the realistic possible outcomes at the last election we ended up with the least worst. I have never voted Labour in my life, and almost certainly never will, but I could live with that result and if I lived in a constituency where it mattered, I probably would have voted tactically to get it. I would not do so with any other current Labour MP in charge, and I wouldn't with Saint Andy of Burnham either.
Labour only ever wins elections when non-Labour voters vote for them. Sir Keir was palatable enough that they could hold their noses and do so. If he goes, so do those voters.
There is a theory that Labour never really wanted Sir Keir to become PM. What they wanted was someone respectable enough to detoxify Labour after the Corbyn years, narrowly lose an election, then quit before the right sort of proper socialist then took Labour back to power. The machinations going on now were supposed to happen after Sir Keir lost in 2024, not after he won.
With the whole Mandelson-Epstein thing I don't really think who is PM would have made any difference; once Mandy or anyone else with a vested interest in playing down their past became a serious candidate for the job (and, let's be honest, he was widely regarded as a good one to put in front of the Donald before his questionable choice of underwear became front page news) then we were always going to end up here.