This has been a cool thread, so I will add, that although we may think we do not look at the neck there is every chance we do through peripheral vision and stage craft.....it has just moved on to us not noticing that we look at the neck as it has become sub-conscious.
we are aware of where our hands and fingers are but we just do not register it anymore because it has now become a habit.
The same can be said for those long term players that look at the neck...it has just become habit.
The way to cure a habit is to acknowledge that there is one, we cannot fix what we believe is not broken or change what we do not know needs changing.
As such it needs discipline, the same applies to a change in any routine, discipline will work it out till the new changes become the new habit.
Un-learn the old and re-learn the new is what needs to happen, and if occasionally the old takes over then that is cool because we truly cannot always justify our actions as some are just reaction within our sub-conscious hard wiring.
But I will relate this story, I worked for many years with a great guitarist, who shall remain nameless, who never ever looked at the neck for any reference.
if he did look at it, it would be through it to look at something else. Different guitars, different tunings he played them all on gigs and recordings and never looked at what he was playing.....but, and this is the funny but, he would create all hell if a venue did not have enough stage lighting.
He would argue to the point of "well 'F@@@ it I'm not going on" if the issue was not put right. No matter how we tried to reason with him that he never ever looks at the guitar, his issue was "not the point because if I did want to look at it I do not have a choice." sort of reply.
I know realise after all these years that he must have had the guitar in his peripheral vision and was sub-consciously referencing it, which is why he would panic in low light or no light situations (no light is when techs darken a stage at the end of a song then bring the lights up, or just puts a spot on the main mic only leaving all others in darkness or low light.)
In all I would say looking at the neck is not an issues unless you make it one, it usually is one of vanity, in as much as it looks un-cool, than any valid musical reason. Another reason is posture, the neck and shoulder can develop issues being always turned to the side, over time this becomes a comfort position when playing as habit to accommodate the neck and shoulder rather than for looking.
The same applies to reading, many player do not put their stands at a correct height and distance. This cause them to 'crane' their necks forward to read, again not a relaxed comfortable position. if you part is to small, re-write/print it larger or wear glasses for the distance you play....reading glasses are not always good for reading what is a few feet in front of you, so a special pair may be needed to accommodate that distance to your stand.
Good luck with whatever anyone chooses to do, and if any of the points I have made raise more questions then PM me and I will help answer them if I can.