This map, taken from the 1973-4 London Midland Region timetable shows clearly that even routes such as the Mid Cheshire, Calder Valley, Atherton and Westhoughton to Southport, and Crewe-Stoke-Derby were regarded as Inter City way back then.
Interesting map, especially as a decade later BR had downgraded the even the Liverpool - Manchester - Leeds - York - Durham - Newcastle trains off the Inter City map
Cardiff trains are via Birmingham, no service to Oxford/ Reading/ Bournemouth (or, if there was, it wasn’t Intercity), nothing east of Sheffield/ Nottingham, but Leicester did have direct services back then (and Southport/ Mid-Cheshire were important enough to be InterCity
(I'm always intrigued and irritated by the way large towns like Barnsley, Mansfield, Burnley and Lincoln seem to be regarded as totally inconsequential by the U.K railway system)
Often just accidents of geography
The ECML happens to go through Retford rather than Lincoln, Great Heck rather than Knottingley, Chester le Street rather than Sunderland, Alnmouth rather than Alnwick
The WCML happens to avoid Northampton and then go through Lichfield rather than Walsall, Preston rather than Blackburn, Oxenholme rather than Kendall, Carstairs rather than Lanark
So we have some “big” places that aren’t served as well as locals would like because the routes chosen in the nineteenth century avoided them, and it’d be horribly expensive to try to “rectify” this today (as more of the country has been built on over the past 150 years/ land prices have gone up significantly, so the logistics and cost of building new lives through the heart of somewhere like Bradford are a lot tougher)
However, whilst I can understand why a station on a “branch” is hard for longer distance trains to serve (and Mansfield being on a line that British Rail closed), the fact that the Neville Hill HSTs to St Pancras went via Westgate (and even some via Doncaster) seems strange when Barnsley or even Rotherham could have been served (unless platform lengths were an issue?)
these were essentially no placing journeys/ dead mileage until they got to Sheffield in the morning (and after they left Sheffield in the evening), so even if going via Barnsley took a lot longer it’d be more beneficial than giving Westgate/ Donny yet another London train (albeit one that’s her overtaken by King’s Cross services)
I’m not saying that Barnsley would contribute hundreds of passengers a day*, but I’m sure you’d get more Barnsley passengers than you would going via Westgate/ Doncaster
(*- after all, why would anyone want to leave Barnsley?)