But as the Liverpool to Birmingham International service is fairly local compared to Liverpool/Crewe to London Euston services it would be ideal to attach them onto that....even better would be to put the local stops onto the new Shrewsbury-Birmingham service providing a stopper and a fast in addition to Wales services
Would make more sense I think to add the local stops into the Crewe to Birmingham via Stoke (which then continues to London for operational reasons) rather than one of the Liverpools - as that is presumably intended as a purely local service.
However I agree that making one of the Liverpools a proper fast (stopping at principal stations only e.g. South Parkway, Runcorn, Hartford maybe, Crewe, Stafford and Wolverhampton only) and adding the smaller, non-inter-city stations onto the other Liverpool (Winsford, Coseley, Smethwick - Penkridge would presumably be covered by the Crewe service) would make sense from the POV of giving Liverpool one proper fast service to Birmingham an hour (and by changing, points south) would be a good idea. Perhaps this could be timed for best XC connectivity from Birmingham to points south?
Not really sure why three trains an hour _off peak_ from Shrewsbury to Birmingham are needed .Peak, yes, but one of the problems of the current railway is over-congestion of the network at off-peak times leading to lower reliability and scheduled waits at signals increasing journey times. If the current service is not adequate capacity-wise why not lengthen it instead to avoid congestion?