Harrogate trains are a total red herring as Advance tickets aren't reserved onto these, and other Northern services arrive sooner in Leeds for those on walk-up tickets. This thread isn't about services such as the ones via Harrogate, and that is made suitably clear in the opening post.
Anyone trying to defend the current practice of showing a false destination just to make people catch a fast train that doesn't overtake a stopping service is advocating for the train company to lie to people in order to delay their journey for operational convenience. The tweet from Aeneas Hart explains this.
Fair enough and I've edited my post to avoid confusion.
I doubt operational convenience is the reason for use of false destinations - it's usually to discourage passengers from taking slower than necessary services. A quick look at a timetable shows most of those Northern services are overtaken. For those that aren't then the correct destination should really be displayed.
The departure boards at York - what is displayed for these services on the main departure boards that show all station calls? The only reason I ask is that the false destination function doesn't appear to be used for these trips, whereas it is for the Harrogate services. Do all train information boards in York station show Cross Gates, or is it only the departure summary board that's shown in the first post?
I have no doubt that staff working at York will be familiar with this and will be able to clarify matters for passengers , as is evidenced by the tweet Yorkie quoted from Ayah Alfawaris. There are pros and cons to deterring people from using services that are overtaken but I hope a better solution is found for those who have reason to ask further questions as a result of an incorrect destination being shown.
Meanwhile, summary boards elsewhere show odd things. At Waterloo East, sometimes Lewisham is implied as the destination for services on the summary board when they actually terminate somewhere else. As such I don't assume that board shows the final destination for all train services - and I'm not averse to asking a member of staff for clarity if needed.