Personally, I would love to see faster services on the longer Merseyrail routes. Unfortunately, I don't think it's very likely to happen for several reasons.
Firstly, Merseytravel aren't interested. The current preference is for "all stations" services to simplify timetables & not to "confuse" customers with a mix of stopping & semi-fast services.
Secondly, I think you would need some serious infrastructure improvements to facilitate express or skip-stop services. A while back, before the 15 min frequency started on the Chester line, I tried putting together a rudementry timetable for the Chester & Ellesmere Port line which had a stopping service every 15 minutes from Hooton to Liverpool (2 starting from Ellesmere Port), overlaid with two fast services each hour from Chester.
What I found is that the fast services invariably caught up the stoppers before they got to Birkenhead, which would defeat the object of running faster services. As a minimum, you would need to expand Hooton to allow overtaking and probably so something similar at Rock Ferry as well.
It's a pity really as I suspect there is quite a bit of untapped potential on this flow. Public perception is that the train service between Chester & Liverpool is slow and it has to be said that in many european countries, a service between two population centres such as Chester & Liverpool would also have a semi fast or regional express to duplicate the stopping service.
Ah well, at least the local bus operator thinks there's a market for an express service between Chester & Liverpool & I will vote with my feet.
http://http://www.merseytravel.gov.uk/travelling-around/timetables/AllTimetables/X8%20Liverpool%20-%20Chester%20(from%207%20September%202014).pdf