Never, ever going to happen as 1 route. Possibly in stages such as Lime Street - Crewe, Crewe - New Street. I don’t know why you’ve included Stoke as it’s not the route taken by trains heading to or from Liverpool.
What he means is that it’s not part of the mainline, you can catch a train from Stoke to Birmingham but it’s pointless if the route is from Liverpool to Birmingham
I don't think at the moment you would ever get a route that length, certainly not from DTG, maybe things will change in a couple of years, I would love to see it though.. I suppose Crewe to Liverpool would be possible with a Pendolino and a class 350, plus a class 66 I guess or Stafford to New Street.