Morally if you've paid full price for a ticket surely you should get a seat over someone who hasn't paid at all?
But my problem with this is that I want to find a theoretical framework which we can use to apply the facts of these two passengers and, by some process, arrive at your conclusion. (If you are really interested, then you'll know that these problems are known as 'normative' by philosophers and others).
Using your example, I'll just challenge your reasoning with two examples:
(I'm not sure where a passenger who hasn't paid anything cae in here - we were comparing prices and discounts a few minutes ago!)
1. I've paid full price for my Temple Meads to Clifton journey and have my bicycle with me. The Guard is coming through selling tix as usual. Someone else has no ticket and is likely to exploit any opp. to avoid paying.
I'd rather stay with my bike, standing.
2. I've paid full price for my London - Edinburgh First Class ticket (actually, its an Advance, so maybe only £60 or so) on a packed Bank Holiday service, with my shoulder bag. Someone else has less limbs than me and a large case and a needy child. I use the word "should" differently.
I'm sorry if I appear to be difficult. Actually, I want to encourage you to think through what you mean by "should" more thoroughly in the hope that we get somewhere useful with this. The Railway regulations are in need of updating, and Regulations which are more appropriate for our world would hepl us all. But a simple "should" just doesn't have the incisive power of better informed ways of analysing rail useage.