I think it all comes down to ones interpretation of DIRECT. Which is why it shouldn't exist. Your primary concern seems to be mileage.
For Any Permitted, direct trains are valid. The shortest (ie, most "direct") route(s) are valid. Mapped routes are valid. The only logical interpretation of "Route direct" is that the most direct route(s), ie the least mileage, are valid, and direct trains are also valid. This should be defined, but in the absence of a definition, no other sensible interpretation is possible IMO.
My belief is that the intention of the ticket is for use between Ulverston and Carlisle on the Cumbrian Coast.
But that's your belief, and even if it is correct, it does not matter what is intended.
Hence the cheaper price, being set by Northern, and the use of the word direct in the way I would understand it (you set off walking directly for your target, as opposed to walking in the opposite direction, and turning round later on).
I don't believe that any route that is no longer than any other route can be considered less "direct" by any definition, especially not in this case where it would be more direct if platforms still existed at Carnforth on the WCML side. Heading away from your destination at any point is totally irrelevant; there is no rule against it, and there is no evidence to suggest that any booking engines have longitude and latitude data to figure that out, and even if they could figure it out it would be utterly pointless as nowhere in the NCoC or RG does it say you cannot head away from your ultimate destination and turn back. What
does matter is the mileage.
I suspect (although I don't know for sure having never had to sell one) that Journey Planner would match my interpretation as well.
I don't believe so. Journey planners have no way to know that you are heading initially away from your destination. If they could detect it and stopped selling tickets as a result then many journeys would become impossible.
In which case I would leave it up to the customer to have the inevitable arguments with the Northern/TPE/Virgin guards on the trains
The arguments may be inevitable but there's only one winner here.
The ticket appears to allow either via Leeds or 'directly' to York. So again could be better labelled, as perhaps just route YORK?
This makes no sense. How can it either be via Leeds or direct? Leeds IS the most direct route, at 31 miles. Harrogate is out of the way. Why is it that you randomly decide Carnforth is out of the way for Ulverston to Carlisle (despite being the shortest route if platforms existed), yet quite oppositely decide that Leeds is out of the way for a ticket from Horsforth to York and that Harrogate isn't out of the way, when clearly Harrogate is out of the way? That makes no sense at all. You are looking at maps and randomly deciding one should be valid and the other should be valid? That's not how any of the rules work, and it's not how booking engines work.
The difference with the above example though being that Horsforth appears to be part of Leeds, whereas Ulverston is most certainly not part of Lancaster.
What relevance does the geographical location of Horsforth in relation to a random station have?
However I quite accept that we should get rid of route DIRECT and replace with something clearer/less open to debate.
It should be got rid of, or defined. But in the absense of that, it can only mean the most direct routes and direct trains. What I am unsure of, is whether it is literally the most direct route only or if the "within 3 miles" rule is included.
And if you buy your ticket specifically for that route, with reservations to prove it, I doubt that they will do a great a deal about it other than complain.