Just want to give my thoughts on Borderlands Line...
As has already been pointed out, it's generally more used to access Wrexham from the southern end, than to access Liverpool from the northern end. This is because the line is not very direct towards Liverpool or even Birkenhead, with a rather around-the-houses trajectory, whereas there as frequent buses making the more direct route through the road tunnels.
As a link between North Wales and the Liverpool City Region, this route has much less going for it than the Halton Curve has. The Borderlands Line links Wrexham with a few small North Wallian settlements and the less dense, western part of the Wirral Penninsula. The Halton Curve could connect Wrexham with Liverpool via Chester and Liverpool South Parkway (for Liverpool Airport). This is actually Liverpool's biggest missing link.
Merseytravel do have long-term designs on this line.
This map from a few years ago seemed to depict that they wanted the whole Borderlands Line integrated into the Merseyrail Wirral Line, complete with third rail electrificaiton; though I've also heard suggestions that it could be standard AC overhead, with new dual voltage being used, changing power at Bidston. There would be new stations at Beechwood & Noctorum, Woodchurch and Deeside Industrial Park. I can't see this happening, to be honest. For a start, even with the electrification and better access to Liverpool, I can't see the line justifying more than 2tph each way. Would the line justify electrification on such a frequency? I know the Ellesmere Port branch of the Wirral Line is only 2tph but it's a much shorter line with proabably a much bigger commuter flow into Birkenhead and central Liverpool. Also, I can't see the Borderlands Line fitting into the metro nature of the Merseyrail system. Merseytravel also have special privilage over awarding the franchise; which it does despite small areas of the system being outside of the Merseytravel area. Adding the Borderlands Line would be a big departure and would challenge this though.
Merseytravel also have a more pragmatic proposal which includes extending the Wirral Line (and so, the third rail electrification) to just the proposed new Woodchurch Station, which I believe is proposed to be sited on Woodchurch Road, right by Junction 3 of the M53. Upton and possibly the proposed Beechwood & Noctorum Station would also be on this branch from Bidston. The advantage with this proposal is that it is entirely within the Merseytravel area which simplifies things somewhat. The stations proposed are well within the Liverpool metropole and so, footfall regarding commuters into the city centre would potentially grow significantly. However, the route is still fairly roundabout to get into Birkenhead and central Liverpool, particularly from Woodchurch and the frequency would have to be 4tph, like the West Kirby and New Brighton branches, otherwise the new stations would not be able to compete with bus services or people just choosing to drive into the city centre. Also, anything less than 4tph would make connectivity from the rump Borderlands Line to Birkenhead & central Liverpool inferior than the current interchange at Bidston. Another, admittedly trivial, disadvantage would be that anyone wanting to access the West Kirby branch stations from the rump Borderlands Line would now have two changes instead of the current one.
Having thought a lot about this line over the years, I personally don't think it should be integrated into Merseyrail whole or at all. Yes, electrification would be nice and so would a higher frequency, though these things probably aren't justifiable. One thing I would propose would be to resituate Bidston Station further east, so it sits at the junction where the West Kirkby and New Birghton branches of the Wirral Line split. There seems to be quite a bit of available land around there, so perhaps a large park & ride could be possible. Ideally, the Borderlands Line would have its own platform here too. This would allow just one change from the Borderlands Line to the stations towards New Brighton, instead of the current two and would double the Liverpool-bound trains through Bidston from 4tph to 8tph, giving the Borderlands Line better connectivity to the greater Liverpool area. This would offer the same connections as Birkenhead North would, without the Borderlines Trains having to stray too far into Merseyrail territory, which would cause operational issues due to Merseyrail's high frequencies and the Bordlerlands Line's well-documented tendency not to timekeep well. Also, if the line speed is increased, instead of extending to Birkenhead North, the Borderlands trains may have a bit more recovery time at the termini than they currently do, which would improve its reliability.