Interesting thread.
I think that asking one person to lead a party of elected representatives (representing very different constituencies) as well as steer a country (and in the UK a union of four countries) is a huge ask, and not very realistic, so the job description is fundamentally flawed.
In most successful management teams there are those who inspire, those who enable, those who drive, come up with ideas, see those ideas through and so on. One person can't do all of that unless s/he has multiple personalities, which might rule them out of the running by definition.
Another problem is that most MPs and cabinet members are ambitious people who pretty much all have big egos, so will probably be waiting for the opportunity to get a better job, and most will also believe that their vision would benefit the rest of us. All of that works against more usual definitions of loyalty, so a leader has to watch his or her back as well as leading from the front. 24/7 rolling news and constant surveillance on SM males it all even worse.
WRT the current leaders, I agree with lemonjam's analysis. I have worked with people who have similar traits to all of them. To take them in turn:
The Badenoch characters get to the top then wonder why they don't have people rooting for them and willing to have their back in a crisis, as they have experience of the ruthlessness that has accompanied the rise to the top. This self-fulfils, as without loyal colleagues the need to run things single handed makes things worse. Nobody chips in for a leaving card when they move on.
The Starmer characters are great in a crisis, but a bit plodding on a day to day level, having been brought up without enough headroom to encourage risk-taking. They believe in process, which can slow things down and be frustrating for people with time-critical ideas, but when they sign off a policy it usually works. Colleagues get irritated by them, but miss them when they leave and they are stuck with one of the others.
Davey characters are fun in their youth, but less so as they age. They organise compulsory 'team building' events, and are fans of exposing ice-breakers that everyone hates. They forget that 'wacky' PR only works with particular demographics and are usually half a step behind what is actually 'cool'. Nice enough people, they are rarely good leaders as they care too much about being seen as 'decent', so won't sack dead weight or make unpopular decisions. Someone has to organise a bigger room for their retirement or leaving party, as they are popular with colleagues.
Farage types see themselves as natural leaders, and rely on confidence to ingratiate themselves with those of similar backgrounds and intimidate those who are not. They talk the talk, and can be very convincing, but often repeat what someone else has just said in meetings as though they had thought of it first, take credit for others' work and always have an alibi when bodies are found. They don't have leaving parties, as they rarely bother to work their notice, but just disappear to a better job, often amongst rumours of having jumped before they were pushed.
. I was simply offering the opinion that it is a lot to expect anyone (of any party) to do well.