Pretty similar experience here : used to play jazz as a teen, we used the Book on rehearsals but we would have DIED before opening it on a gig. I got away from the jazz scene - and the music scene in general - and resumed at 50. Now everyone is on iReal pro.
IME there are pros and cons. Pros : you can play overnight tunes you never heard of and put out a decent act. You can transpose on the fly. You can easily exchange setlists. You can incoporate complex arrangements who need some score (I use my iPad split view to display a PDF from MuseScore). As opposed to paper : lighter, infinite lists, you can play without light (however you cannot play under direct sun

. Cons : yes, you are focussing on the wrong thing BUT normally only in the beginning. After a while, it is more like a safety belt - I barely look at it anymore after a few times I play the tune... You don't train your memory (but maybe you free it for the better ?). You don't learn how to transpose by ear. You are locked up into playing patterns. If you lose your tablet, or it runs out of battery, you're done. And most importantly : as long as you read, you don't really know the tunes and you'll eventually get lost at one point. There's a vid of Ron Carter out there where he makes a point about it
I would compare it with finding your way "the old way" (with a map, asking people, memorizing visual cues etc.) and with a GPS (you can go anywhere, don't have to carry paper, but you don't pay attention and you still need the GPS to go to a place you've been 20 times because you did not have to memorize it).
So all in all : handy, extending possibilities, but limiting your inner abilities (which you actually "externalize" in a device, like so many other ones nowadays...)