What is actually needed as a long-term solution - and what LNER really should be pushing for - is for the backend systems to be updated to support a new flag which would cause booking engines to make a reservation where possible, but still sell the ticket even if it can't.
The way I envisage this working is that when a customer selects an itinerary involving a service with this flag, the default is that a reservation is made. However, if no seats are available, or the customer manually selects that they do not want a reservation, it should still sell the ticket accompanied by a prominent on-screen warning that they are likely not to have a seat on that service.
That logic shouldn't be too difficult to implement in frontend systems, but I can't imagine updating the backend to support a new 'flag' is a small undertaking. So it's understandable it's not been done immediately, but it really needs to be if LNER is to continue with this policy long-term.
Another tangentially related but different question is, are those TVMs set up to be able to reserve wheelchair spaces? If not, some disabled passengers (and their able-bodied companions, if they want/need to be able to sit together!) are probably being issued with entirely unsuitable reservations, which then prevent other passengers from buying tickets.