Another lost election, another Labour leadership contest. And thanks to Ed Miliband’s contentious one-person-one-vote reforms, that inevitably puts the focus back on the party’s members. The most honest objection to the rules introduced under the reforms is that the right to choose the leader should never have been bestowed on the members. Not because they’re cranks or extremists, but because of the party’s composition – by definition, to have the surplus time and energy for monthly meetings and the annual conference puts you in a position of privilege. And this is borne out by the numbers: the majority of members are middle class, their average age 53. Why should that self-selecting band have rights in a two-party political system that others do not?

I think the counter-argument is stronger: that a functioning democracy needs levers of pluralism, identifiable mechanisms by which anyone can influence the makeup and decisions of its representatives. The alternative is the so-called professionalisation of politics, whereby a much smaller group simply determines what the country wants or needs with the help of polling, focus groups and things they hear on the buses they pretend to travel on. This is a clear and straightforward debate, and as such is usually shelved in favour of a series of caricatures.

The idea that the party can’t take power again until all Momentum members are stamped out is simply fanciful

Most commonly, the party is portrayed as having been taken over by a pincer movement of young extremists and the Trotskyist or Stalinist old guard (it is strange to have to look up, yet again, how you’re supposed to tell those apart). Shortly after Jeremy Corbyn’s victory in the 2016 challenge from Owen Smith, a “centrist” in my constituency Labour party described how the radicals who had been painstakingly rooted out in the 1980s had come back, like head lice – as if the hard left was always lying in wait for the host to be weakened.

Even if we accept that 1980s militants all saw their chance and came rushing back, this does not go any way towards explaining the extent of the support for Corbyn. For the interpretation to hold, the militants would have to have not only re-entered the party en masse, but instantly persuaded the so-called soft left to share their agenda.

In 2015 and again in 2016, Corbyn was the only left candidate on the slate. Members had taken their medicine, as they were routinely advised in the Miliband era: they accepted the idea that not opposing austerity, not attacking even corrupt businesses, not protecting public services, was the price of a fiscally responsible reputation, without which the party was sunk. The self-styled pragmatists had had their way, and sunk the ship anyway.

So when Corbyn stood against an array of status quo candidates – more of the same with extra heart (Yvette Cooper), more of the same with extra toughness (Liz Kendall), more of the same with longer eyelashes (Andy Burnham) – his victory should hardly have come as a surprise. A lot of the more lurid exaggerations about the changes to the party’s membership were really just cover for the embarrassment of those who had looked at a party with the same soft-left values it had always held, and failed to predict an entirely predictable thing.

Which brings us to Momentum, which is bedevilled by similar myth-making. At around 40,000 members, the group is just under a tenth the size of the overall party – but a tenth would be ample if it were the revolutionary sect, hellbent on getting rid of opponents, that it’s often portrayed as. There are certainly constituency parties where this picture is correct, where Momentum members did pore over the rule book trying to deselect their MP.

But there are also Momentum groups which are essentially Labour-plus, social and intellectual movements whose members run book groups and club nights as well as attending meetings. They cooperate perfectly well with the rest of the party, since their differences are of taste, not ideology. The idea that the party can’t take power again until these people are stamped out is simply fanciful. By what test would you eject them? “Your food bank fundraiser quiz night had too many questions on grime”?

The view that the party’s composition has to change before it can learn from its mistakes remains fairly niche. Instead, the distortions tend to act as signposts in the leadership contest, all pointing in wild directions: the claim that the members, defined by blind loyalty, will only accept the continuity candidate; or the members, guided by rigid principle, will only accept a woman; or they will only take a northerner. Not only are these precepts wrong, they are also boring, seeking to reduce to a flow chart of predetermined loyalties what is actually a contest of ideas.

The drive to portray Rebecca Long-Bailey as the candidate of the authentic left, and Jess Phillips as the true centre, is more about power blocs than politics – a move to retain power by the existing inner circle on one side, and retake it by the pragmatists of yesteryear on the other. But the other candidates (Keir Starmer, Clive Lewis, Emily Thornberry and Lisa Nandy) are all giving versions of modern leftwing analysis that are genuinely different, and have the potential to coexist and cross-pollinate – because they are about ideas, not control.

That’s the big distortion of this leadership election: the idea that it is dominated by bitter infighting and savage power play. In fact, having transparent debates about competing visions for the future, and then voting on them, is what keeps the party alive.

• Zoe Williams is a Guardian columnist