We’re 11 episodes into showrunner Chris Chibnall’s new regime at Doctor Who now – a complete season, plus the New Year’s special – and I’ve realised that there’s something bugging me.

Actually, there are quite a lot of things bugging me: the endless telling not showing; the complete lack of subplots; the scenes with so many characters in that they look like a publicity shot of the Polyphonic Spree; the dialogue so on the nose that it makes you sneeze. But most of those are obvious, and they’ve been there all along, and either they bother you or they don’t, and if they don’t fair enough. Lucky you. There’s another, though, that it took me an embarrassingly long time to spot – although, in my defence, it is hidden behind both the blizzard of pre-season publicity and the single best thing about the entire season.

Publicity first. The most obvious way in which the series changed this year – certainly the most obvious to normals – was the fact that, for the first time, it had a female lead. The decision to cast Jodie Whittaker as the 13th Doctor was the first thing we knew about Chibnall’s take on the show, and for obvious reasons it got a lot of publicity. Most of this – despite the inevitable warnings from pink-faced men in their 50s who have never really gotten over the fact that Tom Baker doesn’t love them any more that they were now planning to boycott the show – was incredibly positive.

So: that was good. There was some disquiet when rumours appeared that the companion was going to be played by Bradley Walsh, as if the decision to cast a female Doctor needed to be balanced by casting a middle-aged bloke in the part normally reserved for young women. But then he turned out to be just one of three companions, and the show has a long history of getting light-ent types to act, and if Billie Piper, Catherine Tate and Matt Lucas were all brilliant, why not the bloke who presents The Chase?

And lo, it came to pass that when the show was broadcast Walsh’s performance as widower Graham O’Brien turned out to be really bloody good. Many of the series’s best moments involved him acting in exactly the sort of understated way you wouldn’t expect from a gameshow host, and the main arc this season has concerned his attempts to be a father figure to his step-grandson Ryan (Tosin Cole), who is determined to have precisely none of it. The moment in episode four when Ryan is finally about to say something nice to Graham, only he doesn’t get round to it because the latter has just noticed there’s a spider the size of a van on the ceiling, was a) a really lovely moment that b) you couldn’t get on any other show because c) massive bloody spider.

But it’s within the rather sweet, gradual thaw in this relationship that lies the problem. Because you might notice something about the storyline I just described: it’s about two men. What’s more, it’s a story that only happens at all because a female character dies, pointlessly, in episode one. It’s an example of the trope known as “fridging”, in which horrible things happen to a woman, largely to kick off a storyline about a man.

And this is what’s bugging me. Despite being the ostensible lead, Whittaker was given no material as meaty Walsh or Cole. This may have been a conscious choice to de-centre the Doctor a bit, and that may even be a good idea – all that “lonely god” stuff had probably gone as far as it could – but they overshot and made the first female Doctor kind of, well, wet. She just didn’t get to do very much. The impression you’re left with is that Chibnall is simply more interested in his male characters than his female ones.

The Bechdel Test is a way of measuring gender representation in fiction. To pass, a work needs to include a conversation between two named women about something other than a man. As it happens, I think the new season would pass this test – I’m fairly sure there’s a bit where the Doctor and Yaz (Mandip Gill) have a conversation about how to stop a spaceship-eating pig creature. But the point of that test is not that a work can only be valuable if it passes, but that it’s a hilariously low bar, which most films still, somehow, bang straight into.

By the same token: it should have been easy, when casting the first female Doctor, to not end up telling a story largely about men. And yet.