I don't recall talk of a W-N chord.... As for the Shotton curve, it would give a marginally shorter journey time for a through service from North Wales to Merseyside compared with going to Chester and reversing but would mean losing the Chester call, which is also quite a major traffic generator to and from N. Wales.
But assuming that diesels would be banned from the tunnels under the Mersey, ...
There was at one time talk of a freight (steel) chord E-N that would facilitate closure of the Borderlands line to Wrexham.
There was a historic chord W-S, to access Connah's Quay docks that could conceivably be reinstated to provide a Coast to Wrexham route but avoiding reversing at Chester and the single line through Rossett. Problem is the Borderlands track is low speed due to poor-to-no maintenance spend.
Merseyrail did look at a possibility of running diesels into the spare (disused) platform at James St. and turning back there. It was built for steam engines (up to 1903) after all; but no chance of ever running around the loop. In the end I think they decided that overhead electrification of the Borderlands route (either 25kVOHLE or 750vDC Metrolink style) would be a better use for money. And then came the bank bailouts leaving no money for anyone else.
Of course if HS2 were somehow to fall through we would probably see electrification almost everywhere instead, for purely political reasons.