There isn't a valid route Cardiff-Crewe-Manchester-Livepool that I can see, although I'm not sure anyone on the train would know this.
The valid routes Cardiff-Liverpool are shown on maps
- AW+CH
- AW+CV
- AW+JO+CV
- CB+BM+NO
- CB+BM+NR
- CB+BV
- CB+ME
- WB+BM+NO
- WB+BM+NR
- WB+BV
- WB+ME
if you want to check for yourself.
Obviously they can come back via Crewe and to Cardiff.
To spell that out in layman's terms, there are valid routes from Cardiff to Liverpool via Crewe, if you go via Hereford & Shrewsbury and continue beyond Crewe via Chester or Runcorn.
There are also valid routes from Cardiff to Liverpool via Crewe if you go via Birmingham, and these allow you to continue beyond Crewe via Manchester.
What isn't valid, on paper, is going via Hereford, Shrewsbury, Crewe & Manchester. But in practical terms it is almost impossible to enforce this because many TfW services to Manchester have a change of guard at Crewe anyway.
Even if you had the same guard before & after Crewe, and they were to notice that you stayed on after Crewe, I can't imagine there's even a single one out there that would have all of the Routeing Guide maps memorised and would therefore know it's not permitted to mix the two routes.
The public Routeing Guide nowadays only really exists to illustrate what journey planners will offer; on the ground, the "any reasonable route" rule still applies just as much as it did in BR days. And I don't think taking the Marches train via Manchester is such an unreasonable detour that it's likely to be challenged by a guard.
I f anyone challenges it, I'd say it's more likely to be the poorly trained gateline staff you get at places like Manchester Piccadilly, who might wrongly think the ticket is
never valid via Manchester (because London-Liverpool isn't valid via Manchester and vice versa), when in fact it is.