In The Black Archive #7 The Mind Robber, Andrew Hickey opines
There is a common claim in fandom that any story worth telling can be told as a Doctor Who story, to which the obvious retort is that Ulysses (1922) would not be improved by the addition of some Daleks, and Proust's search for lost time would be rather shorter if a man in a blue box turned up and took him back to the time the madeleine evoked.
Now, I suppose it is true that Ulysses wouldn't be improved by Daleks, but it also seems self-evident that the Doctor was in Dublin on 16 June 1904. In truth, like the Titanic, the city was probably thick with different incarnations of the Doctor. And, as a Francophile (there's something for Chibnall), the Doctor would surely have known Proust. Joyce and Proust only met once. One likes to think that the Doctor was there at their meeting.
Equally self-evidently, Joyce must have inserted the Doctor in Ulysses. One could have some fun working out which character (or characters) is the Doctor. Joyce is said to said that were Dublin to be removed from the face of the planet, it would be possible to reconstruct it perfectly from Ulysses. This immediately suggests a story in which the Doctor finds her/himself in a reconstruction/simulation of 1904 Dublin. S/he might realise that it's not the "real" Dublin because this one contains Stephen Dedalus and not James Joyce. There are trillions of planets in the Milky Way galaxy. With an average population of millions to billions, every possible interest, no matter how miche, gets its theme park(s). Obviously, something sinister is going on the Doctor ends up at. It might involve the Daleks.
Much as I would like to see Chibnall do Ulysses in 42 minutes (just think of the Dublin locations), I don't think it's something we would have got even in the 1960s (arguably especially in the 1960s given Ulysses might well have been considered vaguely risque by various parties). It is something that could be done by Big Finish, perhaps if it were pitched to them by Matthew Sweet. It might be a setting that isn't immediately resonant with much of the audience, but that's true of many settings. It didn't seem to worry people so much in the 1960s. And, of course, it is something weird happening in Edwardian Dublin (or a stimulation of Edwardian Dublin or both or the dream world of a Dublin publican), the fact that there are various in-jokes and extra layers of meaning for the Joyceans in the audience is just a bonus.
I am no Proustian, but both the Doctor and Proust are people who have thought very profoundly about time so there are plenty of things for the two to talk about and possibilities for plots (essentially either that Proust wants the Doctor to take him back in time, but the Doctor doesn't think it's a good idea, or vice versa).
Now, not all Doctor Who stories need Daleks or even monsters or even any elements of Fantastika at all. In that sense, there are no stories that can't be told as Doctor Who stories. The question isn't can, but should.
We might perceive that there's a clash of registers. There's more to life than Doctor Who. Joyce was the greatest social novelist of the C20th. Doctor Who is a bit of throwaway fluff for kids. OK, OK. It might be a bit more than that. Against all odds, Doctor Who turned out to the greatest thing that British television generated since the Second World War. OK, not great as a work of art or an aesthetic project in the way that Ulysses is, but great as a machine for producing and examining certain kinds of ideas. (We might, of course, wish that it examined those ideas in different ways to the ways that they are usually presented to us, but we must live with the technoeconomic constraints under which modern commercial television is produced. Joyce and Proust could focus exclusively on art. This is not a luxury that Shakespeare, Davies, Moffat and Chibnall had or have.)
One of things that makes Doctor Who interesting is that travelling with the Doctor is a contact sport. Like life, it's dangerous. And the god guys don't always win, much less win permanently. But no matter how much Steven Moffat might tell us in the novelisation of The Day of Doctor just how terrible the Time War was and how much the Doctor suffered along with everyone else who was involved in the war, Doctor Who still has to operate with a certain register of seriousness. Doctor Who is famously scary. But hiding behind the settee when the Daleks come on only works if, at some point not too much further along, the proper moral order of the universe is (at least partially) restored by the Doctor. The Doctor can't defeat the Daleks permanently, but s/he can at least provide reassurance that they can at least be held at bay over the time being.
So, Doctor Who does do the big subjects, death, particularly, and love, to a degree. It can't do full-on existential cosmic horror directly, but then neither Joyce nor Proust nor Shakespeare do that. (In fact, if anything, DW probably does do better than them in what it can more than hint at with the Daleks and the Cybermen and the Toclafane and numerous other monsters. What makes DW great, is that it is, in part, existential cosmic horror for children.) In fact, we might say existential cosmic horror is fine. It the banal terrestrial variety that is out of bounds. Chibnall, Tennant and Whittaker can explore subjects in Broadchurch that they can't in DW itself no matter how angsty the Doctor might be. Cornell, I think, once said that the Seventh Doctor was the first Doctor he could imagine at Auschwitz. It took until season 26 to have a Second World War story and until series 6 to meet some comedy Nazis including a comedy Hitler. Which goes to show what DW can't do. I read yesterday that some footage from a trailer of an escape in a tunnel from a PoW camp was cut from the montage it would have appeared in in the series itself.
Of course, if you're Lawrence Miles, you might have done some of these things in Faction Paradox novels. One almost longs for the TV show to be cancelled so we can get back to the books (and audios) being good again. Broader, deeper, darker. Although I am not one for automatically "dark" with "good". Even with Leopold Bloom, Joyce no more takes us to the gates of Auschwitz than DW can. Stephen Dedalus might not have flown and spent much of the First World War in Switzerland. (Of course, the Doctor was surely in Zurich in 1917.) History might have other uses for him.
But perhaps wanting to turn everything into Doctor Who is ultimately a failure to embrace adult. DW is good, it is worthy, but there are other things that are good and worthy and perhaps even better and more worthy. Doctor Who needs Joyce more than Joyce needs Doctor Who. Perhaps neither needs the other. But wants is another matter.