LM or Northern would make more sense to operate it (wholly within England, though so is the Shrewsbury - Crewe route).
ATW would still run to Chester via Wrexham (and Warrington).
Regardless, there are much longer ECS movements elsewhere
The franchise is the 'Wales & Borders' franchise and missing off the '& Borders' bit from the operator name was Arriva's decision.
It would probably be more sensible for Northern to have Chester-Crewe than LM, as while neither have crews based at Chester or Crewe, Northern could interwork crew diagrams with Manchester-Altrincham-Chester and their Crewe-Manchester services (and possibly in the future Crewe-Northwich.)
Going a bit off-topic if Manchester-Llandudno was electrified as well there could be a fleet of EMUs based at Chester. If that was done then it would make sense for Stockport-Chester and Sandbach-Northwich to be electrified as then it would allow alternative electrified routes in the case of disruption/engineering works.