Can I just ask when the last regular NW - Liverpool services ran? Are we talking recently (since privatisation) or is it back in the BR days?
I think the direct North Wales-Liverpool via Runcorn finished like most useful through trains in 1967 with the run-down of regional services (even then it was not frequent).
There were also NW-Birkenhead direct services (avoiding Chester) and of course Shrewsbury-Wrexham-Chester-Birkenhead direct services.
All cut back to shuttles from Chester.
Meanwhile, the Marches route offered through trains to Liverpool via Crewe until about 2000, alternating with Manchester.
The Liverpool trains were reduced to about a couple and then stopped completely (to give Manchester an hourly service).
ATW have never served Liverpool, but I think they retain Crewe-Liverpool rights of some sort.
There was a short-lived attempt by FNW to run Chester-Warrington-Liverpool, but this was cut back to Warrington-Liverpool and I believe may be axed after electrification (becoming electric Manchester-Liverpool).
The CLC world once ran Wrexham-Hawarden-Seacombe (Wallasey), but was diverted under BR to New Brighton and then cut back to Bidston.
Either way there has never been a through service via this route to Liverpool.
Whichever way you look at it, Wirral and Liverpool have a huge population but no direct services to North Wales.
The main link is of course Merseyrail from Chester, but this is a relentlessly local service with many stops and a long journey time for the distance.
On the other hand it does have a 4tph frequency.
You have to live here to realise that Manchester and Liverpool, with Chester, are the business and leisure destinations for North Wales, particularly North-East Wales which is in easy commuting distance of both.
I can't describe how irrelevant the Cardiff connection is, except to the political class.