9xxx trains are supposed to have the highest priority, to ensure making and exiting the core on time (and ideally in the correct sequence), but it doesn't always happen and a late 9Yxx WGC to Sevenoaks service can sometimes get put behind the Moorgate even though it means being stuck almost all the way to London.
I suspect a lot of this is down to automatic route setting and perhaps not enough time to manage trains manually, to plan for a train to pass a slow/delayed service near Hatfield, Potters Bar, New Barnet etc. If there isn't anyone to step in, it will just run as the computer sees fit. I have no idea if the systems in York have changed on account of the new signalling between Hatfield/WGC and Hitchin/Biggleswade, but long before the changes there have been cases where trains are made to run fast (either to ensure the next working isn't delayed, or maybe to ensure crew get to another station quickly to not delay other trains), but never actually pass a service ahead so may as well run as booked.
But, this isn't relevant to class 379s and I can't see how their introduction will change any of the above!