On the Bournemouth to Manchester run there is a lot of passenger turnover at New Street. Anecdotally I'd say about 66-75% of the arriving passengers disembark, but that's not in any way scientific.
If (for example) the train continued through to Coventry (let's electrify one of the sidings adjacent to the Leamington line for turnbacks if necessary) then I suspect that in itself wouldn't inconvenience many people coming from the north - though I'd probably be one of them...
Though that wouldn't help passengers needing to go to Leamington or further south (could those run via Solihull to save a path on the Coventry line? But then that would disconnect Coventry and Birmingham International from direct trains to/from Leamington and the south...).
If (for example) the train continued through to Coventry (let's electrify one of the sidings adjacent to the Leamington line for turnbacks if necessary) then I suspect that in itself wouldn't inconvenience many people coming from the north - though I'd probably be one of them...
Though that wouldn't help passengers needing to go to Leamington or further south (could those run via Solihull to save a path on the Coventry line? But then that would disconnect Coventry and Birmingham International from direct trains to/from Leamington and the south...).