Going back to when North Wales and South Wales services were worked by different TOCs, First North Western's Chester depot signed the route as part of a more regular (roughly 2 hourly) Holyhead to Birmingham via Stafford service. Wales and West/Wales and Borders Crewe depot signed the route as a diversion between Crewe and Shrewsbury. Under Arriva Trains Wales most of the Birmingham - Holyhead services were diverted via Wrexham, with just the 1 remaining Stafford service in each direction per day, worked by Chester drivers and Crewe guards (Chester guards on a Sunday). Crewe drivers kept it as a diversion route, and for cross-depot cover for the Chester worked services, but AFAIK it's not actually been used as a planned diversion route since about 2013 (there have been very occasional ad-hoc diversions since then, but it's extremely rare). Diverting via Chester is much quicker and easier to get paths for - and much more staff are competent that way.
Fast forward to today, with route learning for drivers only recently reintroduced after a hiatus during Covid there's very few drivers left who are still competent on Stafford, and there are much higher priorities for TFW's limited staff right now.