Well there was a time when I couldn't play anything unless I had the music in front of me, and the little A5 size books proved invaluable: gradually over the space of 10 years or more, I have improved my "ear learning" - forced myself to do it - amd now can get through most tunes sessions without music ion front of me, whether I previously know the tune or not. Part of it is being more familiar with my instrument, part of it just learning the stuff, developing brain- and muscle-memory. (Try to carry on a conversation while still playing the tune!) I am aware of some people who just will NOT take their eyes off the written music still ("in one eye and out the other") despite having played the same tune x000 times. They DO need to "throw away the crutch". And one of the problems of the "ossified session" is that some people do go on to automatic pilot - play slow airs far too fast, lose all musicality in certain tunes. I have given up on one of the sessions referred to as it is far too repetitive and unwelcoming of any attempt to introduce any new tunes.
I do struggle to learn words of songs anything more than about 5 verses long, and I do prefer to sing a wide variety of songs rather than a very limited number: hence I will use song words sometimes, but hopefully will use the words as a backstop and know how the song goes before I launch into it. Nothing gets up my nose more than those folk who sit and wait until their turn comes round (they can see it coming a mile off!) and then faff around deciding which of the 100s of songs in their files they will do. If I do need to take lyric sheets to a session, I'll decide on a short list of 3 or 4 and just take those with me.