I think this is the whole point about the bad design of HS2: it doesn't integrate well with the existing network. Most TGV services in France run into existing stations and this is true of Germany, Belgium, Holland and so on. Lille may be an exception, but it serves as a major interchange between several high speed services.
London requires at least 3 stations on HS2, with services calling at all of them. If Euston were a through station towards Stratford then there would be useful connections to HS1, many of the places South and East of London and also places served by DLR. Though even this might not be the best solution and a link into services South of the Thames would be very useful to many passengers.
If HS2 integrates well wth local services then although the headline speeds might be slightly lower, the overall travel times of many more passengers will be greatly reduced.
This applies to other places as well as London - Leeds, Birmingham, Sheffield, Nottingham stations all present travellers with inconvenient and time consuming connections from existing services.
For this reason more than anything else, HS2 needs a rethink, not the blind following of an idea that seems increasingly dodgy for all sorts of reasons. This blind dogged thinking is typical of UK government and the Civil Service, creating the inflexibility in project development which, for example, results in the loss of £10bn on NHS IT.