I'd imagine one issue with only having one central station is how you accommodate future changes in traffic - particularly growth. A few main stations have had extra platforms added over the last few decades: Marylebone and Birmingham Moor Street, for example. But that doesn't happen that often, because most big central stations -as an inevitable consequence of their own existence attracting people to live and work next to them - have no free land around them. St Pancras has been totally rebuilt/had new platforms added in a way that is pretty sub-optimal in terms of walking distance. Euston will get the HS2 platforms - at massive expense underground.
If you insist on one central station, then the problem gets worse because that station will inevitably act as a huge draw for businesses etc. and therefore over time see exceptionally dense building all round it - and probably a dense network of metro tracks underneath it - making it almost impossible to find anywhere to build new platforms/tracks when passenger growth happens.
In real life, very often the solution to improving services ends up being to build new through lines (Birmingham Snow Hill) or convert existing lines to metro/tram (Manchester, Newcastle), or even to build brand new lines (Crossrail). Thameslink is a special case where you had a nearby railway that was working well below the capacity it could have with infrastructure improvements - so the improvements were made and some services diverted away from their existing terminals. A long time ago, capacity was created at Kings Cross by diverting some services to Moorgate. Birmingham Curzon Street is an example of this too - no room in the existing stations for all the new trains, so a new station will get built instead - massively more cheaply than it would be to expand the existing main station. I'm sure one of the drivers behind most of those schemes would have been the difficulty adding any capacity to the existing main stations. But most of these solutions are not compatible with any insistence that you want everything to run to the same central station.
I think, even if you had money-no-object plans to build a single station in any of our big cities today, you'd inevitably find that in 20-30 years, you're forced to abandon the idea and start running at least some trains to other stations in that city.