Do you have any loading figures for those? At peak times a 156 is able to take around 200 passengers without being classed as overcrowded. Unfortunately, there's a situation where some PTE area services get 4 carriages because they get a loading of around 200 while non-PTE area services with higher loadings struggle with 2.
From my casual observation, the Liverpool-Airport services load less than the Norwich and Scarborough services out of Liverpool, but more than the Newcastle.
But the one peak time train I use (0816 ex Lime St) is absolutely stuffed even at Lime St, with boarding problems and overtime at every intermediate stop.
Westbound, people just congregate at Piccadilly/Oxford Road and get the first train to Liverpool, so there is a more even spread between the 3 semi-fasts.
Intermediate station usage at Wavertree/St Helens Jn/Newton le Willows is fairly low compared to Parkway/Widnes/Warrington on the CLC route.
The service is pretty reliably run by 156s, unlike the Liverpool-Blackpool which has descended to shabby 150s most of the time.
Doubling up is very rare on either service.
The TP Newcastle service is lightly loaded to Huddersfield.
People heading for Yorkshire don't care which train they get at Liverpool, but those going to Manchester still evidently prefer the Piccadilly services.
The 3rd world state of Victoria (sans trams and virtually every other convenience) doesn't help, of course.