Ok, so that would free up a path then if Birmingham-Scotland on HS2 means the classic Birmingham-Wolverhampton-Scotland service is withdrawn; means Wolverhampton would lose its through services to Scotland though.
As planned it couldn't do that, unless you are willing to remove the Bristol/Reading-Manchester through services forcing changes in Birmingham (or diversion of Bristol-Manchester away from Birmingham, eg. via the Welsh Marches). Only a tunnel into Curzon Street from the south west would allow Manchester-Birmingham-Bristol services to use HS2 and services from Reading/Southampton/Bournemouth are likely to continue needing to use New Street.
Rail travel from Basingstoke and southwards using the existing service patterns to get to Old Oak Common (used Paddington for times) and then onwards to Birmingham (using Euston for times) is comparable to the existing XC services. Going to Manchester is faster. (Feel free to check).
As such the only place which is likely to lose out is Oxford (Banbury and northwards would still have other services).
If you were to create through services from the South Coast to Old Oak Common you'd make the journey quicker (cuts about 15 minutes from the journey time). Given that XC services wouldn't be that useful for many, you could use their paths South of Reading for a Paddington service.
Yes it would mean a change of trains, however it would be faster and it would be more frequent for most other XC destinations other than Birmingham and places South.
You then create a Reading/Birmingham service and everyone changes at Birmingham. You mainly only impact on passengers to/from Oxford.
However it gives you one extra path an hour northwards from Birmingham for the suggested service. You could even join up the two service so that it runs Reading to Holyhead.