This is why I was saying TfW should not operate this service. It needs to be operated by an English operator because they have to answer to the DfT, and can be challenged by English MPs and English voters. Unfortunately, we have unbalanced devolution in the UK. so TfW are answerable to the Welsh government and not to the DfT and not to MPs or voters in England. Basically TfW don't care two hoots about the services they run in England.
TfW operates services in England under DfT purview, including frequencies and performance levels, just as it has been since the ATW franchise was let in 2003 (by the Westminster SRA with WG input).
English MPs have a route via the DfT to the TOC owner (TfW the WG agency).
The Liverpool service was hatched in the coalition period as a joint Merseytravel/WG/Network Rail project under the Liverpool City Region deal done by George Osborne, which funded the Halton Curve reopening and the initial ATW train service to Chester.
Northern were at the time in a hopeless position to operate the service, and WG saw it as the first step to extension into Wales (it already reaches Wrexham).
Neither LM/LNR or MR ever had any interest in a Liverpool-Chester DMU service.
Operated with 197s it works well with TfW's fleet plans - they are still not through the transition period yet, though.
TfW's northern operation is significant and Chester/Shrewsbury are major revenue generators for them.
The 197 fleet, like the 175s before them, is based in Chester which last time I looked was in England.
Manchester, Liverpool and Birmingham are key to the TfW network, not some awkward foreign branch lines as you seem to suggest.
TfW has its faults and has been low on performance for too long, but I think their hearts are in the right place.
Currently they are also not in dispute with ASLEF, which some would say was a benefit compared to the DfT TOCs.
I agree there are times when TfW appears to be a Welsh national entity serving parochial Welsh interests, but it isn't really.
There are UK parliamentary committees which discuss such cross-border matters, it's not wholly a Cardiff Bay operation.
And Network Rail is not devolved to the WG, not even to the extent that Scotland is.