Merseytravel did have a plan to extend Merseyrail to a new terminus at Woodchurch, just off Junction 3 of the M53. It included a new intermediate station between Upton and Bidston at Beechwood. For whatever reason, they parked it a few years ago.
Part of the problem with that end of the line is that it doesn’t take a particularly direct alignment towards Birkenhead and Liverpool. It would need to justify a fairly frequent service (I reckon 4tph) to effectively compete with the local bus services.
Partially electrifying the line also compromises the convenience of passengers changing to/from the rump diesel service. Bidston currently offers 4tph into Liverpool and 4tph to Bidston. The new extension would have to have 4tph to retain the convenience for changing; even then, West Kirby branch stations become two changes away, although that direction is obviously much less important.
So, for, me, it has to be either all or nothing. To be honest, I don’t think the line is a good fit for Merseyrail. It goes too far out of the area. I think the likes of Southport and Chester are the absolute limit, distance-wise for a high frequency all-stops service with no onboard toilets. Even those are pushing it a bit.
My ideal preference is for it to be re-extended to Birkenhead North with an extra track added between there and Bidston Junction, complete with layout alterations so that it can be operationally separate from Merseyrail. Birkenhead North offers double the frequency into Liverpool that Bidston has plus direct services towards New Brighton. Borderlands services could perhaps skip Bidston and Bidston could even be closed or relocated if its role as an interchange were to end.