The Edinburgh example isn't ideal for this, as it's a botch that was badly done by Avanti when LNER introduced the first trial of single leg pricing. As others have suggested, the right thing to do would have been to have route via Carlisle instead.
Is this Avanti's fault? LNER withdrew the "any permitted" tickets in 2020. They have now removed almost all of their return tickets between Scotland and southern England without changing the route codes for any of the "any permitted" tickets.
Unless there's some crucial difference between a London-Edinburgh ticket and a London-Haymarket one which I'm just not seeing, they could easily have changed the former's route back to "any permitted" at the same time, and solved the problem at a stroke.
Incidentally, I think "via Carlisle" tickets would be a bad idea for this route. It would cost around as much as the "via York" ticket, so would give customers nothing apart from needless complexity. It's a better idea than "Avanti only" tickets, but not by much.
I was suggesting that for every route that the routing guide permits, there should be an inter-available ticket that is sold that can be used on that route.
It does not seem right to me that there can be a route that the routing guide says that I can use, but I have to use a particular operator in order to do so.
Perhaps it's a matter of perspective? To me, you can use the routeing guide (in combination with other data such as the timetable) to find out what you can do with an "any permitted" (or otherwise unrouted) ticket, and gives some information about how to understand tickets with other routes. If you want to work out the permitted routes you need the route code for a ticket, just as surely as you need the start and finish stations.
On that basis, the question of where an "any permitted" London-Edinburgh ticket can be used is moot. The flexible tickets all have "via York", "Avanti only" or "Lumo & Hull only" routes, so the permitted routes are based on one of those.