If the route was wired to Basingstoke, even if only into the bay platforms, then you'd have 2tph EMUs doing the stoppers and if 99s or similar get intermodal work from Southampton, those freight services can utilise the wires as well once on the line. Ditto for XC services if bi-modes ever takeover from Voyagers, but the former two would bring the most time-saving potential.
I do wonder, if there was wires to Basingstoke and extra capacity if it could then work that the units run Newbury/Basingstoke via Reading or better yet batteries/wires to Bedwyn so 1tph could be extended to there.
The ideal would be 3tph, although I suspect that could be at the expense of the potential to reintroduce the 0.5tph for XC.
Although in a post HS2 world it might be off peak Newbury/through Basingstoke share a 1tph Paddington path (either by or being 0.5tph but having a Reading service when there's no through service, or by splitting/joining at Reading/Reading West).
Being able to access a direct service from (maybe as far away as Poole) SWR stations to connect with HS2 services could be very helpful in generating passenger usage for the railway.
Southampton to Old Oak Common direct (obviously would carry on to Paddington) would be something like 70 minutes, even with a 20 minute change, thats Southampton to Manchester in 2:30 vs 4:15 currently, even if you wait a full hour because it's the wrong hour for the direct service to Old Oak Common that's still 45 minutes less time traveling (more likely to be a 1:15 sooner arrival time as it'll be 30 minutes adrift from the direct XC service, which would mean rather than the 7:15 (XC) getting in at 11:29 the 7:45 (GWR/HS2) would get you there for 10:15, so an extra 30 minutes in bed but still an extra hour in Manchester).
OK, we might lose a few minutes vs the XC times for the local stops, but maybe 6 minutes and maybe gaining back 1 minute if we can get some small line speed improvements, however less than 10 minutes, so not a big difference overall in the times above.
Yes, I went there as to why there's should be a direct Paddington service from/through Basingstoke, it's just not that London is the justification (although places like Bramley (Hampshire) and Mortimer would also benefit from the direct London services)