A good leader never asks their people to do something they wouldn’t do themselves. Hold others to the highest standards, by all means, but only if you have equally high expectations of yourself: otherwise you may command obedience in politics but never respect, and over time even that grudging compliance may come laced with contempt. And so it is, less than two years into power, for Keir Starmer.

Nobody in government emerges well from the story of Peter Mandelson’s journey to Washington, and that includes Olly Robbins, the Foreign Office mandarin sacked for not telling Downing Street that its chosen ambassador had set off fire alarms inside the vetting process. Robbins could arguably have saved himself by kicking this intensely political decision upstairs, albeit to a prime minister famous for not really doing politics: he could have just let Starmer choose between the public humiliation of telling the Americans that the man he wanted to send into their highly classified midst was a potential security risk, or the gamble of sending Mandelson anyway but with added guardrails.

Admittedly, even that wouldn’t have been as simple as some of Robbins’s critics make out. It might look ridiculous from the outside, but the vetting process relies on people being able to confess the most excruciating things in confidence, and the taboo within Whitehall on sharing any aspect of it is real. Even Cat Little, the senior civil servant who finally uncovered the failed vetting in March, says it took her three weeks of conferring within the system to establish that she was allowed to tell the prime minister about it.

But with the benefit of hindsight, choosing to keep everything within the Foreign Office’s jealously guarded fiefdom nonetheless looks like a rare misjudgment, for which the ambitious Robbins paid with his beloved job. Unfortunately, that makes the contrast with Starmer, a man whose misjudgments are mostly paid for with other people’s jobs, if anything more glaring.

Less than two years into this administration, the bodies are piling up to the point where it’s hard to dispose of them with dignity. The final grenade Robbins lobbed on his way out of the Foreign Office was the revelation that Downing Street hadn’t just sought a foreign posting for Mandelson: it also seemingly inquired if there were any ambassadors jobs going spare to cushion the fall of outgoing spin doctor Matthew Doyle, a man who is to high-level diplomacy roughly what an elephant is to ballet. In the end, Doyle was stretchered out into the House of Lords instead, only to lose the Labour whip shortly afterwards when it emerged he had campaigned some years previously for a friend charged with indecent child images offences to become a councillor. Once again, warnings were seemingly overridden: the SNP MP Stephen Flynn says he wrote to the prime minister flagging up the connection and asking him not to ennoble Doyle, but was ignored. To be caught trying to wangle jobs for the boys once, in the teeth of warnings that later turned out to be prescient, is unfortunate. But twice? That seems more than careless.

It’s hard to overestimate the soul-crushing impact of all this on Labour MPs. Angry and frustrated, some are wondering why on earth they gave up perfectly good jobs for this life of impotent embarrassment. Rumours are flying about ministers on the verge of quitting: like sunflowers turning to the sun, ambitious backbenchers are visibly swivelling away from Starmer, trying to ingratiate themselves with whoever might be coming next.

Angela Rayner and Louise Haigh, both of whom were cut loose from the cabinet – the former over her taxes, the latter when it emerged that before going into politics she was charged with insurance fraud over a reported lost phone – made high-profile public interventions this week, with Rayner’s sounding suspiciously like a stump speech. Reports of even loyal cabinet ministers challenging the prime minister over the implications of Robbins’s sacking, meanwhile, reflect a fear that going to war with Whitehall will poison any remaining hope of Labour achieving radical change in power: civil servants who think they’ll be blamed if anything goes wrong are more likely to retreat into foot-dragging, back-covering obstruction of anything too bold.

What unites all the people Starmer has dumped along the wayside is not that they were blameless. None were saints, all made mistakes, and some were not up to operating at the highest level. But the same looks increasingly true of him and yet he clings on, sustained by the fear that it could always be worse: that with Andy Burnham not in parliament, and none of the contenders bar Ed Miliband obviously qualified to lead the country through the economic shock now brewing in the Gulf, the outcome of any coup remains worryingly unpredictable. Much like the strait of Hormuz, Downing Street is essentially blockaded, with no obvious way in for a new prime minister and no obvious way out for the old one.

That could yet change if the foreign affairs select committee – whose chair, Emily Thornberry, knows a thing two about jobs for the boys, having been dropped from the shadow cabinet on election day to accommodate Starmer’s old friend Richard Hermer as attorney general – finds any evidence to contradict Starmer’s public insistence this week that No 10 did not put pressure on the Foreign Office to appoint Mandelson. Ironically, the prime minister’s fate may now lie in the hands of the last person before Robbins to lose his job over all this: the former Downing Street chief of staff Morgan McSweeney is expected to face questions on Tuesday over allegations that he told Robbins’s predecessor to “just fucking approve” the posting.

If you’re losing track by this point of which faceless apparatchik exactly got fired for what when, then you’re not alone: even one of the MPs on the committee observed halfway through Little’s testimony that there had been so many sackings it was hard to keep up. But one thing is clear amid the confusion, and it’s that this affair reveals almost as much about Starmer’s character as it does about Mandelson’s. The thing about pushing body after body off the back of a sledge is that every time one hits the snow, we see the driver a little bit more clearly, until he’s the only one left. If he’s still blaming everyone else even as he hits the oncoming tree, then that wasn’t leadership, but the failure to recognise its absence until too late.

• Gaby Hinsliiff is a Guardian columnist

• Guardian Newsroom: Can Labour come back from the brink?
  On Thursday 30 April, join Gaby Hinsliff, Zoe Williams, Polly Toynbee and Rafael Behr as they discuss how much of a threat Labour faces from the Green party and Reform UK – and whether Keir Starmer can survive as leader. Book tickets here