Since this is a Speculative Discussion thread, could I ask the reverse question to the thread title and ask which parts of the Merseyrail network could be taken over by Transport for Wales and by Northern Trains.
An interesting question. Working clockwise...
Southport makes sense as Merseyrail since it is a terminus distinct from any Northern services. Northern services that terminate at Southport would need to reverse to use what is now Merseyrail, meaning inefficient journeys amongst anywhere the change would bring connection to.
Ormskirk could see extensions of Northern services, but it would not be far before the passenger volumes to Liverpool would be better suited to Merseyrail. On the Ormskirk line, extending Merseyrail seems the more likely future direction.
Headbolt Lane has already seen Northern cut back so it is unlikely there would be a reversal
Hunts Cross strikes me as an odd terminus and does seem to involve avoidable interaction between Merseyrail and Northern. However, I do not know if the Merseyrail service could be cut back to Liverpool South Parkway (and maybe pushed on elsewhere) with Northern having more trains serving Hunts Cross. Electrification of the CLC would allow Northern to add capacity so it is not a completely lost cause to limit Merseyrail. IF development fills in the gap between Widnes and Halewood, a new station and more Northern EMUs would have a further case.
Ellesmere Port/Chester could each be changed. Sending Merseyrail to just 1 of these would increase frequency for the victor. I would assume that means Chester getting more Merseyrail. In such cases Hooton to Ellesmere Port would go over to Northern. However, that would need more trains to Warrington/Runcorn and I do not see either route being electrified. The result would be less efficient, even if the extra connectivity from Ellesmere Port Eastwards might help some users.
Neither West Kirby or New Brighton have other services.