It seems to me a bit odd that in 2017 there are still "blackspots" like this. Why is this? Are there no "train describers" on these sections?
Legacy signalling, ultimately.
To use the Hammersmith branch as an example (purely because it's the one I'm most familiar with), no train descriptions are passed between Hammersmith OZ (opened 1951) and Edgware Road OP (opened 1926) signal cabins, and all signalling outside of the two controlled areas is under automatic signalling, with no intervention possible from the signallers.
When trains depart Edgware Road westbound for the Hammersmith branch they 'lose' their TDs because there is only one place they can go*, Hammersmith. This information is of no use to the Hammersmith signaller, and in days gone by there were, of course, no train describers on any of these platforms.
Similarly, on the eastbound, no TDs are sent from Hammersmith as a hangover from the days when all trains went to Whitechapel/Plaistow/Barking (delete as era-appropriate) and the Circle line trains were just that.
What data is available is very much a bodge and, although most of the time it is useful enough, it becomes completely redundant as soon as any out of course working is in place.
Essentially, the timetable is fused with the limited Trackernet data available and this is what powers the new platform DMIs and other 'real time' info. As trains progress along the branch they pass through different radio cells which can determine the approximate location, and it is this data that forms the basis of the departures. The 'next train' boards at Hammersmith are manually operated by the signaller at OZ cabin.
*It is possible for trains to be terminated at Goldhawk Road and run directly into the siding at Hammersmith. However, this is not a timetabled move and is often only decided at the last minute for service trains, or offered as an option for additional trains, if platform working at Hammersmith cannot cope with the additional train, or if it was running straight into the depot and such a move would ease congestion.