It's more about capacity west of Southampton - and possibly platforming there too.
undamentally, if we have 2tph to Salisbury and 4tph to Southampton and Portsmouth - of varying stopping patterns but hopefully two fast to each - then that should be a good London service.
The issue is that you move closer, and the semi-fast routes (terminators at Basingstoke, Guildford etc) also require uplifts - but tend to be more peak/commuter in pattern. And yet they will act as local, school etc connectors too.
Other problem is that Clapham, Woking, Basingstoke, Winchester, and SAP (less so) - are all busy. It's hard to have a true fast. And would it be full? I would wager more people travel from Winchester to London than Southampton Central to London (the latter is busier but has more services to elsewhere and locally) - so would HSR be useful? Also west of Southampton is a trundle but with no easy solves - so you're not really doing much for Bournemouth and Poole.
I think that if there was a HS line to Salisbury with then a link to Southampton/Bristol/Exeter (probably not all the way, just enough to get a decent service) it would allow you to bypass the congestion and allow those services remaining to be increased in frequency.
Basingstoke is likely to still be fastest going via Woking, however Andover would likely be faster via Salisbury and the new line. Which would probably mean that Salisbury/Exeter wouldn't need to go via Woking and would only get as far as Basingstoke (maybe Reading).
XC could likely be the only fast service from the South Coast to Basingstoke (giving Eastleigh a more frequent service), however could run 2tph all the time (as the Cornwall services wouldn't need to go via Reading West so frequently, enabling the increase in XC services).
Portsmouth could see some services route via the HS line however that would need a fair amount of new track from the HS line to where they could connect.
You could get a reasonable level of service, maybe something like:
- 3tph to Exeter (one continues to Plymouth/Cornwall, until the Dawlish Avoiding Line is built and then all 3 would go to Plymouth with a few going to Cornwall)
- 3tph to Southampton
- 3tph to Bristol
- 2tph to Basingstoke (stopping between Salisbury and Basingstoke)
Whilst no where near as much as HS2's 17tph that's still 11tph, before there's consideration for anything extra like routing some services to Weymouth via Yeovil.