I'm going to answer my own questions, and although I can't be certain of the exact outcome the answers I'm providing are probably fairly likely and are based on general principles rather than on details which may be a decade away before they are decided upon.
The likelihood is that the extra platform space freed up by moving the long distance services to the HS2 platforms will mean more local services. What that looks like in detail is unknown, but it's fairly safe to say that there would be more local services. As such there will most likely be benefits beyond just London.
Given people's preference to get places faster people will opt to use these services, however people are also cost sensitive and so if the ticket costs have a large cost disparity between the existing and HS2 ticket prices then no one will use them.
Given the large capacity of the HS2 trains there's little advantage in seeing the prices high. However let's for a moment assume that they are set higher there would still be some who use the HS2 services. Even if this is only 1 in 50 people that's still upto 5 people who aren't using the current XC services per service.
That means that there's more XC capacity for more passengers. However the closer to the existing ticket prices the HS2 tickets are the greater the number of people who will swap to HS2.
If we assume that an existing ticket was £50, then if HS2 charged £150 they would get only a few people out of 1,000 existing passengers (an income of £600). If they dropped the cost to £75 then they'd probably get 100 people (an income of £7,500). Whilst if they set the price at £50 they would get 999 (allowing for those who have decided not to use HS2)
of those 1,000 people (an income of £49,950). As such if you were HS2 what Rick price is most likely? I would guess the £50 one, which is the same as existing.
As such the numbers of people moving from existing services to HS2 is likely to very high, meaning that for those who's stations are served by existing services and not HS2 would likely have more capacity available to them.
Again, assuming similar ticket prices which would generate the most income as detailed above, chances are that there's going to be a lot more capacity to the airports.
Although there is likely to be more services for London, there's also likely to be services to other places (such as suggested in my response to the platforms). Therefore there's likely to be benefits to other places, even if these haven't been defined yet.
The likelihood is that the extra platform space freed up by moving the long distance services to the HS2 platforms will mean more local services. What that looks like in detail is unknown, but it's fairly safe to say that there would be more local services. As such there will most likely be benefits beyond just London.
Given people's preference to get places faster people will opt to use these services, however people are also cost sensitive and so if the ticket costs have a large cost disparity between the existing and HS2 ticket prices then no one will use them.
Given the large capacity of the HS2 trains there's little advantage in seeing the prices high. However let's for a moment assume that they are set higher there would still be some who use the HS2 services. Even if this is only 1 in 50 people that's still upto 5 people who aren't using the current XC services per service.
That means that there's more XC capacity for more passengers. However the closer to the existing ticket prices the HS2 tickets are the greater the number of people who will swap to HS2.
If we assume that an existing ticket was £50, then if HS2 charged £150 they would get only a few people out of 1,000 existing passengers (an income of £600). If they dropped the cost to £75 then they'd probably get 100 people (an income of £7,500). Whilst if they set the price at £50 they would get 999 (allowing for those who have decided not to use HS2)
of those 1,000 people (an income of £49,950). As such if you were HS2 what Rick price is most likely? I would guess the £50 one, which is the same as existing.
As such the numbers of people moving from existing services to HS2 is likely to very high, meaning that for those who's stations are served by existing services and not HS2 would likely have more capacity available to them.
Again, assuming similar ticket prices which would generate the most income as detailed above, chances are that there's going to be a lot more capacity to the airports.
Although there is likely to be more services for London, there's also likely to be services to other places (such as suggested in my response to the platforms). Therefore there's likely to be benefits to other places, even if these haven't been defined yet.