Think from the players perspective, what are they trying to do from corners? 9 times out of 10 they are aiming for the centre halves or the big number 9 if they have one. Position yourself where you can get a clear view of where the ball is most likely to go, which is towards the heads of the biggest players. Most teams will be just aiming for the same player every time at the lower levels and will have the same corner taker from both sides.
Stay on the goal line? For me definitely not. You can’t see pushes or holding. And you are inviting the goalkeeper to aggressively push their nearest opponent (which, of the many, is probably the most common problem I face in non-AR games).
You most definitely can see pushes and holding. I've missed very little from that position. It's an equivalent view of 95% of the in-the-box stuff, but even closer and provides a better view of anything right in the goal mouth.
As opposed to the 'on the field' position where I would have missed every single ball in/out. I wonder how many goes would have come as a result?
Now, there is one thing I forgot to mention - you also need to constantly think about what's happening. In some games, standard positioning is wrong. Sometimes you need to adopt a funny position at a GK or a FK because the manner of fouling is occurring in a way that you can't see it from that normal position.
If I had a no-NAR match but fouling seemed to occur in a blind spot - or the player I needed to watch was not-visible, then I'd consider changing. Because it changes priorities and likelihoods.
As I mentioned before, off the goal line provides me with the only view of some things, and equivalent but alternate view of almost all fouls, and a poorer view of some things.
Standing outside gives me a better view of some things (breaks, ball far side of goal), and equivalent but alternate view of almost all fouls, and no view whatsoever of the most significant things which are fairly likely to occur. That seems like a no brainer to me.
The only way to police the corners was from side on. From the goal line I would not have been able to see many of the players, let alone what they were up to. Before the corners I often started behind them close to the goal line. When the corner was taken I typically went to the side of the penalty spot at the near post ( because the players were in the goal area, in some cases mostly on the goal line!) And then I moved back and to the side as the ball landed (my diagonal) or to the D (if corner from the right). The one I remember most ended with the ball on the floor in a crazy melee on the edge of the goal area, I stepped back while it was happening, I had to watch feet, saw no offence, but once the ball was cleared one defender had a sore head - so I missed something as 10+ players crowded the ball! Very difficult.