I think the last few posts back up Graham's original post. The problem is the impression gained from the enormous variability in ticket checking, from several times in one journey to not at all.
I think I’d come to completely the opposite conclusion.
We started off by talking, to some extent, about people new to rail travel. If they get the idea that they can have their ticket checked anywhere, anytime and most importantly, randomly, it might stop them getting the idea that they can get away without paying.
The problem with regular, predictable checks is that people might see ways to avoid them. On another forum we were recently discussing the Severn Beach line and how some passengers have sussed out that if they sit or stand in a particular part of the train, for a relatively short journey, they can avoid paying their just dues.
The local RPO team have become aware of this and keep an eye out for just such behaviour.