The BBC’s Question Time programme has a new editor. She’s Hilary O’Neill, a no-nonsense journalist who was most recently deputy editor of the News at Ten and is a former colleague of mine on the Today programme.

Her appointment turns out to be one of the last made by the outgoing director of BBC News, James Harding, who announced this week that he is standing down. But it is, say insiders, a reflection of the greater importance Harding and BBC News want to place on Question Time; and O’Neill underlined that in the press release. She described Question Time as “the highest-profile… public debate programme in the UK”, adding that “in these tumultuous political times it’s never been more important to hold politicians to account.”

She inherits a show that, like many others, is only just starting to get to grips with the tumult around it. The recent flurry about the content of BBC Radio 4’s Today reflects the crisis in our politics and the challenge of getting something useful out of Westminster-based interviews. But interrogating decision-makers is still what journalism needs to do, and the flagship programmes of the BBC are where the nation is watching and listening.

Question Time has an audience that’s usually at least four times greater than that of Newsnight or Channel 4 News, and its format gives it the ability to spark exchanges between leaders and voters that are illuminating and memorable. The BBC is right to try to renew its relevance.

The current run of Question Time shows that David Dimbleby, who is 79 this month, remains adept as a chairman, but the internal BBC discussion about his successor, which has been going on for a decade or more, will at some point need to come to a conclusion. More immediately, the problem is how to re-cast the panels.

It was striking how a particular generation of politicians were the ones who brought the programme to life: Shirley Williams, Tony Benn, Charles Kennedy, Michael Heseltine, Ken Clarke. Now the main parties produce too many frontbench clones who never knowingly deviate from the talking points of the day, and lack the ability to speak human. As the Tory party drifts to the right and Labour to the left, there is more confrontation and less enlightenment.

This is manifested in the studio audiences. Corbynistas, Nats and Ukippers tend to make more noise than the retreating Blairites or Tory moderates, and some editions – notably the one from Plymouth in the summer – have had an ugly atmosphere. There is nothing wrong with fervent believers getting stuck in, but the absence of angry claques of the open-minded shouldn’t put centrist positions at a disadvantage. I’ve spoken to former panellists who now turn down invitations because of the venom of the responses to them in the studio and on social media.

As an attempt at leavening the mix, the invitation list has long included not just politicians and journalists but celebrities and comedians. The footballer Joey Barton was entertaining as a one-off, as was Russell Brand debating with the ubiquitous Nigel Farage. What is revealing, though, is how few of them make a return appearance; and these serious times should demand a more serious Question Time.

And there is an obvious gap in the programme’s casting: it shies away from experts. This is not about allowing the forces of the establishment to browbeat the public, as Michael Gove feared during the EU referendum campaign. It simply involves putting on air some people who know their subject inside out. There has, for instance, been an inability to tackle the Brexit negotiating positions of the Conservatives or Labour – partly because there are obfuscations they share. So why not add an EU expert from academia or a think tank who can expose the evasions? Similarly, scientists rarely get a look-in on Question Time panels. This is not about filling the panel with hidden partisans or purveyors of centrist goo: rather, it’s about challenging views that are at odds with the facts and bursting the balloons of wishful thinking.

There’s a logic here that the programme might spend more time on major topics. Good. It also might usefully thin out some panels. In fairness, the producers have had to juggle with the multiplicity of minor parties who merit exposure because of their parliamentary representation; but the result of the last election showed a strengthening of the big two parties and should result in some of the smaller groupings being given fewer outings. There is, of course, evidence of how a concentration on the people with power can result in excellent programmes and the highest ratings: the leaders’ specials during the election campaign were examples of what the format can deliver.

Just consider how simple that is. It is an audience of voters with one leader at a time; and it breaks through in a way that multiparty debates sadly don’t. It’s also an invitation that no party leader can dodge. In this year’s campaign editions, Theresa May was rattled by persistent questioning from a nurse about NHS pay, and Jeremy Corbyn was irritated by interrogation about Trident – and both were illuminating moments. Similarly, it was on Question Time that David Cameron delivered his most impassioned performance of the EU referendum campaign.

More of these specials would be welcome, and they point to the opportunities in scheduling too. It should be possible to think of Question Time being placed at 9pm every week, and allowing the excellent This Week to move earlier too. That would be a resounding statement by the BBC about the importance of current affairs, now more than ever.