Birmingham - London is less than half of the EBW patronage or in other words, the majority will still need the existing service.
Are you counting people who disembark at Birmingham International in that figure, since there will be a profusion of HS services to there as well.
What you are proving is the dangers of over capacity - the beauty of the current service is that flows cross-subsidise both ways - the demand isn't enough for 3tph to Birmingham or Manchester only either.
Since frequency drives demand not capacity the result will be less patronage. So much for "serving the intermediate stations better".
The as I understand it the following "intermediate" non HS2 stations have services on ICWC to London using trains to one of the HS destinations:
Wolverhampton (off peak 1tph)
Sandwell and Dudley (off peak 1tph)
Coventry (3tph)
Rugby (1tph)
Milton Keynes (2tph)
Watford Junction (1tph)
Wilmslow (1tph)
Crewe (1tph*)
Stockport (3tph)
Macclesfield (1tph)
Stoke-on-Trent (2tph)
Right, a single Wolverhampton Train would call at:
Wolverhampton, Sandwell and Dudley, Birmingham, Birmingham International, Coventry, Rugby, Milton Keynes Central, Watford Junction, Euston
That Provides the current off peak level of service to all West Midlands Specific non-HS destinations apart from Coventry.
A single Manchester Train would call at:
Manchester Piccadilly, Stockport, Macclesfield, Stoke-on-Trent, Milton Keynes Central, London Euston
That provides the current level of service to Macclesfield and brings MKC up to its current level of service.
This means that 6 paths have been replaced with 2, with the following losses:
Coventry goes from 3tph to 1tph
Stockport goes from 3tph to 1tph
Stoke on Trent goes from 2tph to 1tph
Wilmslow looses its service entirely (currently 1tph).
Crewe goes from 3tph to 2tph (but may gain compatibles).
You propose we throw away two additional paths an hour to give Coventry 3tph instead of 1tph when every other destination sees no change in its frequencies whatsoever?
Wilmslow would take a path simply to serve it without any benefits to any other stations, I am not convinced that it could support the service effectively by itself.
Stockport would require two additional paths to maintain its service and with the Manchester-London journey time being so quick, it becomes drastically faster to double back via Manchester on the High Speed line, which will have for already stated reasons, buckets of capacity.
The four paths per hour that we save by doing this could be used for numerous things that might bring benefits to the "damaged" stations.
I think it is far better overall.