And surely it would be better to extend these trains to Rainham and terminate the Thameslink service at Gravesend?
In theory yes, but the problem is is that Medway commuters rely on the vast interchanges on the Woolwich line, the DLR, Jubilee line and Crossrail all intersect or are very near to the Woolwich line, the Sidcup line doesn't offer anything like that at all, also Thameslink need Gillingham depot, because Gravesend/Hoo Junction has apparently been safeguarded for a future Crossrail extension which may not happen for another ten years at the earliest!
What should happen is that they should extend the new CX to Dartford service via Lewisham and Woolwich to Gillingham, in addition to the Thameslink service, have the CX service skip Northfleet, Swanscombe, Stone, Slade Green, Erith, Belvedere and Dockyard and have the Thameslink service call at those stations, that way everyone wins.
I have heard rumours that after 2019 Thameslink will review the Rainham service, as they have taken into account the effect Crossrail may have, will usage at certain stations near to Abbey Wood or Woolwich Crossrail fall? Or will people change at Abbey Wood for Crossrail, it has been predicted that demand for Crossrail will be pretty high from day one and let's not forget that the Abbey Wood branch will be the one that will have services that will actually reach outer West London, Heathrow and Reading, not to mention that Crossrail from Abbey Wood to Farringdon will be much quicker than Thameslink to Farringdon via Greenwich.
For me I've resigned myself to sitting on hard plastic seats on a train that sounds like the sound effect for a UFO in a 1950s b movie and a much longer commute for the forseable future until things change