Yes there is. It’s North Kent East Junction. The route exists east of London Bridge and is how the journey would be done by crossing over there. If Charing Cross services end up on diversion via Greenwich that is where they will cross.
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You are right in that media and general reports said the route was “severed” which is either just downright false or a misrepresentation of the state of play. Really the reason it’s not done is because it is would add one huge conflict across one of the biggest parts of the track in the country, which is exactly what the Thameslink programme (and the Bermondsey flyovers) was meant to resolve. This became almost immediately devalued though when Thameslink was sent down to Rainham as something of a last resort.
The present arrangement with the Thameslink<>Rainham service is much much better than trying to squeeze a Charing Cross to Greenwich service through the North Kent East Junction area would have been.
Both directions of a Charing Cross<>Greenwich service would have to use the single Southwark Reversible line to access the Bermondsey Diveunder (used in the current timetable by Thameslink trains going from Greenwich towards Luton, and yes used in the other direction today by trains from Charing Cross to Charlton diverted via Greenwich). This would have used twice as much capacity through North Kent East Junction, eastbound being the killer as it prevents any other moves to or from Cannon Street while a train crosses over.
By contrast, the inbound and outbound Thameslinks are able to cross through the whole North Kent East junction in parallel to each other.
All you lose timetable wise vs running the whole 6tph Greenwich service to Cannon Street is the ability to hypothetically run a parallel train from New Cross to Cannon Street on line 3 (with the Greenwiches on lines 1 & 2).
It's usually pretty smooth in practice, although yes, there are occasional delays from the conflicting moves.
And it's not much worse than the originally proposed Thameslink to Ashford via Chislehurst service. This would have been a diversion of the Cannon Street trains, admittedly at peak times only, and would have locked up almost as much of the North Kent East Junction area getting to and from the slow lines via New Cross. It not being possible to get from the Fast lines at New Cross to the Thameslink core without using Metropolitan Junction west of London Bridge, which was never on the cards.
