There are definitely large sections of the Underground network where a timetable is useful, on the Bakerloo north of Queens Park, on the Central west of North Acton and east of Woodford/Hainault, the Richmond and Ealing branches of the District, the Mill Hill East branch, the Circle, the H&C, the Uxbridge branch of the Picc, and north of Harrow on the Met come to mind.
It would be great somehow to take the set numbers from the WTT and combine this with realtime information to produce an app that would be able to tell me that, for example train 440 the 19:35 from Watford has been cancelled. Given the limitations of data which power the APIs (especially at the start of the day), I’m not sure how this could reliably be accomplished.