Groundloop,
I am always happy to stand corrected, so you are right in that voltage is no longer a concern, as the LGVs, Chunnel and HS1 all use the same. I was under the impression the voltage was different in the tunnel.
However, there is a previous safety restriction about the trains needing to be able to split in the middle and for one half to exit the tunnel. As I understand it, the new Class 407 ICEs have fireproofing to enable them to meet updated regulations, but the TGV sets used in France & neighbours do not.
D-Bahn want to run a service through the tunnel which will then split / join at Brussels to form shorter sets.
Although it always seems good logic to have surface links to airports, they are not as big a traffic generator as the cities they serve - in other words, as a rail destination, LHR is much smaller than London. Therefore, running services through the tunnel, even to a mega-hub airport, which terminate at the airport, is going to be a commercially weaker proposition than running straight through to St Pancras (I'll leave hs2 for another debate).
Of course, some Eurostar services could be diverted into the new airport, and then could proceed to St Pancras, but that would add to journey time and create a security / immigration challenge. This just isn't such an issue for rail services through AMS, CDG, FRA etc as they are all operating within the Schengen zone.
The current APD regime favours people taking Eurostar or budget flights to airports like CDG or AMS in order to make cheaper long haul onward journeys, but it does not work the other way round. A new airport of this size would not be a low cost facility by any stretch of the imagination, so it would have to charge a hefty PSC, making it less competitive, compared to what we have with the devil we know at LHR.
Therefore, I stand by my point (with slight factual correction) that a new Thames Airport would not be likely to attract significant enough numbers of passengers by rail to make a direct link through the Chunnel viable.