My point about the Crewe to Chester shuttle is that it exists solely because faster and more direct trains have been diverted on a dogmatic meander through extra Welsh calling points that add almost an hour.
Birmingham to Bangor without change (via Wrexham) is around 3h14-3h19. The direct route can be done in 3h01 including 33 mins of festering at Crewe and Chester for the two extra changes.
I take your point on the journey times, but the reality is that the paths on the WCML and into Manchester Piccadilly were recast some years ago and it is they that dictate the timings of trains in and out of Chester, and specifically of the TfW service between North Wales & Manchester and the Avanti service between North Wales/Chester and Euston.
Running the Birmingham service via Crewe (and ditching the shuttle) would mean two trains (One Avanti and one TfW) within 10-15 minutes of each other in either direction between Chester and Crewe and then nothing for 45-50 minutes, assuming the shuttle was removed.
It would halve the connection opportunities at Crewe in one foul swoop unless you continued to operate the shuttle which would in turn require more rolling stock.
It’s easy to say it’s “political dogma” but the revised paths on the WCML and into/out of Manchester are a significant factor as well.