I am going to provide my definitions (disclaimers?) before sharing my views.
- in my piano and guitar worlds, this happens only once. It is what I do with new sheet music that I have never laid eyes on before.
-It's what I do when I have an audience quietly seated in front of me, and they are listening to me play. They're also seeing me sweat...watching my efforts to appear calm with every wrong move, bad note, memory lapse etc...and probably hearing me curse (under my breath) on a really bad day. Generally, I memorize music for these occasions.
Was the guitarist at the pub providing background music for people who were engaged in enjoying food, drink and conversation along with his music?
If the guitarist gigs regularly at that pub or other local spots, he is more concerned with setting a mood that results in satisfied customers and repeat business for the establishment.
No tux required, since it inhibits a run to the bank before the check they gave him for playing bounces.
Since it was unlikely that he was being watched by all the people all the time, having scores at hand made it possible to play a much wider assortment of pieces than he could have memorized for the occasion. As long as there were not long pauses as he turned pages or searched for the next book or piece of music, I think it was practical and acceptable for him to read from scores. I do the same without reservation or shame.
As a listener , if I do not buy a ticket, pay a cover charge or go to a venue especially to hear a certain musician play, I have a hard time considering it a true performance. I relax and enjoy the live music for the rarity it is these days in affordable restaurants and bars.
As a player of any given piece in your repertoire. Once you have memorized a piece, it is sometimes a difficult thing to revert to using the music. The printed music is almost a distraction. This can be an unsettling experience. I suggest that once you have scheduled a performance and decided on your program or playlist, commit to using the score (or not) for each piece. Stick to those decisions and for that engagement practice each piece with (or without) the score. At performance time go for broke. What you have is what you have in reserve. Play the memorized pieces from memory. Play from the scores, the pieces you have rehearsed consistently that way. Hopefully, things will go more smoothly for you.
If your aim is to become a master player, limit the time(s) you play for inattentive audiences. If they aren't listening, you are not receiving the full experience, support and feedback that you need on your path to artistry. The players you most admire are probably not spending much, if any, time playing in pubs.
Hope this helps, whatever your chosen venues. All the best!