Of course they do in this instance as Chester is actually in England and does not come part of their remit.
There's the paradox.
WG DOES have responsibility for most services through Chester as the cross-border franchise is not being split.
What's more, the Deeside proposals are linked to the joint cross-border business and planning groups, including things like the Halton Curve.
It works both ways, with industries like Airbus and Toyota being in Wales but with a significant chunk of their workforce coming from England (Chester, Wirral).
Vauxhall at Ellesmere Port is an example of travel the other way.
My two neighbours work in Liverpool and Wilmslow.
Yet another irony is that a station in "Welsh" Saltney, would be just in England, much like Knighton on the Central Wales line.
Much as it offends Plaid enthusiasts and dike-builders, it is a single economy.