Philip
On Moderation
When is this for? Post HS2? None will go via Northampton apart from possibly a few peaks. Liverpool will be covered by HS2 so anything that exists from there is going to be stopping south of Crewe. Nothing is going to miss Birmingham International either on the Birmingham route, nor Coventry with your last service, that is daft.
Post HS2 is many years away yet even for the section south of Birmingham, this is focused on the railway before HS2 begins.
I think Coventry can make do with a two-per hour frequency to London in addition to the Cross Country and WMT services which also serve it, perhaps Birmingham Intl should also be served by two Avanti London trains rather than one. There is no need for 3 trains per hour from London to Coventry/B'ham Intl though and so it'd be useful for London-Birmingham NS passengers if they had the option of a service which only stops at Milton Keynes and no where else.
I think Northampton is big enough to justify having an intercity service to London, if there is a path available. Either one of the Birmingham or one of the Manchester services would be good as these would still have two fast services in addition to the slow which goes via Northampton.