A lot of talk on here about capacity uplift seems to assume captive services will still run. Maybe you'd better speak to the posters concerned.
HS2 has little connectivity to the rest of the network. Trains will run off one branch towards Liverpool and Scotland, and off another on a short branch ro Sheffiled and towards Newcastle, and that's it. No additional connections to the south, south west of east. Some extraordinarily myopic features built in eg no northward connection to the line from Sheffield, despite the Sheffield-Leeds service being one of the worst between nearby major cities in the country: no Birmingham-Liverpool HS2 service, leaving instead an almost-all stops service taking 1 hr 45 mins to cover 80 miles.
Your worries about adding to the cost of HS2 somewhat miss the point. We should be working out what the most urgent problems on the network are, and addressing those. Funny how cost is always wheeled out as an excuse not to do something which deviates from the current HS2 plan, and yet HS2's proponents seem entirely comfortable with the astonishing growth of the cost of fulfilling the current plan.
It has been proposed that XC consider changing where in Birmingham that their services go so as to be closer to the station at Curzon Street. This alone will aid with transfer between services and so would enable that people would be more likely to change trains.
When considering whether people will do so you have to look at the amount of time that they will save, given that Birmingham to Leeds will be an hour faster, even taking 30 minutes off of that to allow for changing will make it worth doing for quite a few people.
I fear that you are trying to make HS2 fix too many problems and therefore trying to have direct services from everywhere to everywhere. The problem with this is that you can always find another place which misses out. Let's assume that we did run services from Southampton, what about Portsmouth and Brighton?
Anyway much of the South East would be able to access Old Oak Common and therefore improve journey times. Let's take Southampton to Manchester as an example, it currently takes 4:15 to travel on the XC services at a frequency of 1 train an hour, so how long will it take if we go via HS2?
We can't be sure at this stage, as there's no timetables, however the following gives us a fairly good guide:
Existing services allow you to travel between Southampton and Paddington in 1:30.
Euston to Manchester will be 1:10 using HS2.
Allow 20 minutes to assume that you've just missed the previous Manchester HS2 services.
Given that it'll take a few minutes to get between Old Oak Common and Euston/Paddington that then gives you your allowance for changing trains.
That results in a 3 hour journey time, it also allows you to travel twice an hour.
Now whilst that requires 2 changes of trains the risk of missing your connection at either location is fairly small. We've already allowed for a non perfect connection at Old Oak Common, even if we did so again at Reading (on the southbound journey, on the northbound journey it's less of a problem as Reading to Old Oak Common would be a lot more frequent) it would add a further 30 minutes. This would still be 45 minutes faster.
If we were to do the same to Birmingham it would be closer.
Southampton to Birmingham is 2:40.
We'd still need the same maximum 1:50 to get from Southampton to being on HS2 service and then 0:49 minutes to being at New Street. As such you'd probably not bother, however there's the option to do so if there's problems on the XC network.
Now whilst you'd see more of an improvement of there was a direct connection with HS2, however how would you do so?
If you added a junction then that would then impact on the ability to run as many services, especially if it was away from a station.
Even if you didn't impact on the capacity from the maximum, where do these services run between? Does Southampton justify a direct service to Manchester, what about Leeds?
Given that HS2 services would be able to carry 1,100 passengers over 400m (2.75 seats/m, which as aside is comparable to 2.7 seats/m of the class 80x's, which would result in 1,076 seats, we could quibble over 24 seats if we like, but it's likely to be there or there abouts), there's unlikely to be need many services running, especially given quite a few of the existing passengers wish to go to other places served before you reach Birmingham.
As such you're likely to be better off changing trains to get there faster than waiting for the next direct service.
Whist there could be a case for building a junction to allow SW services to connect to the HS2 network, there would need to be new trains to run the service, as such it's not as easy as just running the existing trains. Therefore the overall picture needs to be considered before building something which may not be usable for some time.