We also have a strict 'No Phone or iPad on stage' philosophy! In my opinion if you don't know the chords or the words, then you are not ready to play the song live!
while i agree with the 2nd part of that statement (and i think 80% of weekend bands should realize that statement
), i personally perform with my phone that has lyrics.
when i gig, i have a rep of about 400 songs and growing. at this point in my life, i can't remember the lyrics to 400 songs all the time. chords i usually have no issue with, except the occasional tricky song or part.
if my band had a set list of 30 songs prepped ahead of time for a specific gig, i'd learn the words no problem. but for what i do, where requests are plentiful, i'd rather have the lyrics there so i can perform the song well, rather than start, forget a verse, make something up, or similar.
often i get a request for a song not even in my BandHelper app, and i google the lyrics if i have heard the song before, and figure it out right there. people are more forgiving with chords than words, and i'd rather have the words there to be solid on at least that. melody and chords i usually have no problem with.
on a typical night, i would perform 40 - 50 songs in 3 hours, all ranging from that 400+. i just can't remember that many lyrics. i know some people can, and that's just amazing to me.
one of my usual duo partners had the "no phone" approach in general. so he'd keep his ipad in his guitar bag. but then someone requests a song he didn't know the words for. he then turns around, opens the gig bag, powers on the ipad, waits for it to boot, gets the ipad mic holder, sets it up, puts the ipad on the stand, connects to the internet, searches for the song, then plays the song. yup 3 minutes of dead air at a live gig.
to me, if you're in that situation, having it there, ready to go, is much better than "proving" you can gig without it, but then taking all that time to use it at some point.
of course we may be talking about completely different gig situations, but just some insight on why i personally choose to always have my phone and lyrics there.
i think placement and device choice is important too though. many colleagues of mine use a 12.9" iPad, set up directly in front of their face like a TV, completely blocking their face from view of most of the audience. some use their device chest level, or even knee level, so it's not blocking their face, but then they are performing while looking down the entire time. i try to put my phone - a small device - just below chin level, and i have it angled as flat as possible (parallel to the ground) so that from the audience POV, it's a thin line of something, not blocking my face.
eyes and vision are different for everyone, so i don't judge their needs. but as a performer, if i watch someone and all i can see is the full back of an ipad, it leaves a little to be desired.