The BBC deserves credit for standing its ground on an election debate, and luring Jeremy Corbyn to take part. Its portfolio of special campaign coverage has been sensible and well-scheduled. But the format of the Cambridge event – which degenerated at times into a shouty muddle – shows the need for fresh thinking about debates and about television formats with an audience.

This election the broadcasters faced the obstacle of a prime minister who said from the outset that she wouldn’t take part in debates. This has, of course, been the traditional view of any party leader starting a campaign with a large lead in the opinion polls – hence no debates involving Margaret Thatcher or Tony Blair. It was only in the close contest in 2010, when Gordon Brown had nothing to lose and David Cameron spotted the need to gamble, that we saw the debut of a proper television leadership debate in the UK.

Crucially, those programmes involved just three politicians: Brown, Cameron and Clegg. They drew enormous audiences – more than 9 million compared with Cambridge’s 3.5 million – and they had a significant effect on the campaign, not least in the Liberal Democrat surge after Clegg’s strong performances. But by 2015 Cameron was agreeing to only one debate, and he made plain his preference for it to involve as many as possible of the opposition parties.

This coincided with the broadcasters recognising that the UK party system was fragmenting, and they also needed to reflect the devolved nations. So into the mix came the SNP, Plaid Cymru, Ukip and the Greens; and that recognition of the smaller parties has continued in this campaign and has provided the cast list for both the BBC’s and ITV’s primetime election debates.

The trouble is that a 7-way debate makes bad television. The search for a killer soundbite triumphs over any attempt to make a coherent argument, and a moderator has to fight against everyone talking over each other and interrupting when it’s supposed to be someone else’s turn. Mishal Husain coped valiantly, but turning this into a coherent format is beyond anyone’s powers.

It also doesn’t necessarily achieve fairness. Plaid Cymru, which won just 181,000 votes in the 2017 election, is grossly over-represented in a UK context compared with Ulster’s absent DUP, who won more votes and more seats. Ukip, with one MP elected in 2015, is on the same footing as the Conservatives and Labour. Editorially, it’s a nasty trap for any big party. For a PM or potential PM, having six opponents ranged up against you risks becoming a blood sport; and Theresa May was on a lose-lose, because she might have been battered even more by turning up than by her absence.

This is compounded by the challenge of getting a studio audience that is, and sounds to be, balanced. Sky and Channel 4 fared better this week than the BBC, though I suspect that there is an inevitable greater noise factor from youthful Corbynites than from ageing Conservatives. But given that Question Time is a valuable and accepted part of any campaign, there’s doubt about how necessary audience participation is in other programmes. One of the brightest young talents, Sky’s Faisal Islam, was left stranded by a structure in which audience members didn’t follow up their line of questioning, but where he was supposed to leave the substantive interviewing to Jeremy Paxman.

So for the future: broadcasters should stand by the need for debates as part of the mix. A prospective prime minister should regard participation as a democratic duty. But, within the context of being fair to minor parties across the campaign as a whole, let’s bid a kind farewell to Leanne Wood and to Paul Nuttall and possibly to Caroline Lucas if there isn’t a Green breakthrough in 2017. Don’t allow audience claques to form in studios, and ponder whether the public is needed at all in some cases. And that’s because the other lesson from this campaign is that the forensic single studio interview, as performed brilliantly by Andrew Neil, can be one of the most useful tools for viewers in deciding where to cast their vote; and that is the simplest format of all.