What an interesting theory! Thanks for opening this one up!I'm fairly new to singing in front of people & tend to keep my eyes closed when singing - Sorry! I'm pretty sure that it's because I'm easily distracted.
I've been trying to open them & communicate with the audience more, but when I see the people (even friends) in front of me, my memory for the words just disintegrates & I stumble through the song & gain little satisfaction from the singing of it.
With my eyes shut I can concentrate on recalling the next line or where I am in the story of the song. This is probably just nerves & hopefully will be rectified by time & experience - I hope!
As to learning the words, I usually keep my eyes open otherwise I'd crash!
Other cats?