I do think that long-term, any HS lines that terminate in London should all do so at the same terminal. If we're going to build an entirely new country-wide fast rail network, let's not spoil it by making everyone have to make 45 minute connections across the tube!
45 minutes? I could crawl between Euston and St Pancras in that time! Wack in a travelator and we're talking about a transfer that is as quick as Thameslink or MML to the Victoria line at Kings Cross St Pancras (and less walking!)
I quite agree that trying to change the existing lines is a unlikely prospect, but if we are serious about building a meaningful HS network in this country, there's no excuse not to build it into the same London station.
So France isn't serious about building a meaningful HS network? They didn't even tweak it to make TGV Nord and TGV Est terminate in the same station, but instead two near each other...
As for excuses, how about:
1)a single London terminus for High Speed trains to all over the country (including the South Coast as well as Kent, Europe, North and West) will feed too much traffic onto the tube network for adequate dispersal of traffic through central London (even if each line had their own OOC-style 'get a third of the traffic off' station).
2)a single London terminus for High Speed trains would have too many platforms.
3)security checks for the Channel Tunnel puts paid to easily and practically having a through station with through running and no/few terminal platforms.
4)the geography and demand patterns likewise prevent that sort of set up
5)huge expense for little gain
Sure, 45 minute journeys on the tube (is there even one inter-terminus journey in London that takes that long?) is not good, but a couple of minutes on the tube, or a 10 minute walk, or a 5 minute travelator journey isn't really a hardship - the latter two transfer times could well exist in the same station (and certainly do in airports) - especially if the station had most of the capital's intercity trains serve it!
The trip from Old Oak Common would only be ~19 minutes and with phase 2 trains would run direct there anyway.
As long as 19 minutes? Heathrow Express takes 15 minutes between Paddington and Central today. Take 4 minutes off for Paddington-OOC, and wack it back on for being on the slows and stopping at Ealing Broadway and Hayes & Harlington if (when) HEx is taken over by Crossrail. That gives 15 minutes.
And maybe HS2 Ltd have won in convincing the DfT that a Heathrow link is a waste of pretty much everyone's time - I've not heard anything about Heathrow in the HS2 pre-announcement teases...