Common sense for Merseyrail to take over the local services run by Northern within greater Merseyside: ie Wigan NW to Lime Street; Runcorn (or South Parkway) to Lime Street. The potential is there to fully integrate them with the network via the Wapping tunnel, with the dual voltage provision already agreed. Electrification at least as far as Warrington Central is a no-brainer. But the diesel lines (and the through route to Manchester) are not going to be easily integrated.
With respect, I think that the existing Merseyrail electric system should remain an an (almost) self-contained network. If you used the Wapping Tunnel to try and funnel trains from Wigan, Newton Le Willows, etc. into Liverpool Central, that would create a situation every bit as bad as the Castlefield / Oxford Road /Piccadilly section in Manchester. Delays miles away from Liverpool could cause huge conflicts with paths through Liverpool Central & Moorfields, etc.
Also, as happens on the Merseyrail Chester line, they would almost certainly want to give priority to all-stations stopping trains, making it difficult for pathing longer distance fast & semi-fast services; the Blackpool & Cheshire Lines "fasts" might even cease, making many journey times longer.
Moreover, diverting services to Central would lose the very important connectivity with long distance services at Lime Street, and I very much doubt that Central could cater safely for lots more passengers.