It helps in multiple ways.
1) as noted it can often be used as the ticket.
2). It does not require a cell network (I think loss of cell network /internet access is why folks don’t trust cell phones, it is not the phone but the connection that is the problem)
3). The numbers on the ticket may allow the agent to look up you ticket info.
4) You can (with time) print out a copy of the ticket on paper (I did this once in england at my hotel. I emailed the concierge and he printed them and gave them to me)
Case examples: last year in London on the way home I had issues with my boarding pass. Delta screwed something up and would. not print my pass. Part of the problem was a conflict with my trip the previous year and my flight into Germany. The agent at the counter could not find my history. I happened to have my ticket info and copies of my boarding passes from 2017 and the one to Germany in 2018. They called those up by the info on in the photos showed his manager who overrode the system and I had my pass in 10 minutes. Originally the agent was worried that it could take “hours” to find the problem. Of course I as still SSSS but at least I made the flight.
Case example two: I normally print out paper copies of everything I need and put it in a folder by day so I grab that day’s paperwork and I am all set. For instance if I am taking a train checking into a hotel, and then taking a tour I will have in that days envelope a copy of the train tickets, the reservation and the tickets for the tour, that way I don’t have to scramble. But somehow I put the tickets in the wrong days pouch and took them a day early. I had them in my back pocket and sat in a wet bench and they got wet. So I needed new copies. I sent them by email to the concierge and he set the bellhop up to my room with them.
Case example 3. I was had a car scheduled to take me and my elderly father to Heathrow from our hotel (MUCH EASIER on Dad the public transit). But somehow they where not sure of where to drop us at Heathrow, A quick glance at the ticket and away we went,
Case Example #4. I was taking. A taxis to my hotel in Paris. I speak very bad middle school French but that SHOULD get me buy yo get yo my hotel as I can speak/read French out loud fairly well (not sure what I am saying but I can pronounce the words written in the page pretty well). Problem was the taxis driver (like many/most in Paris) was not French and spoke about as bad of French as I do, I showed him my reservation he typed it into his GPS and off we went, similar thing happens on the next two taxis trips in Paris. And I even had an issue getting the correct train station.
Case Example #5. First trip to France in 2017. Staying at the Hilton? never the airport as it was train into Paris on my last night in France and a relatively early flight out, I asked for a wake up call and a shuttle bus to the airport. The Concierge asked some questions. I showed him my ticket info on my phone and he figured out my schedule and when yo get up and when yo take the bus. And where to get off the bus at.
So in just two trips having readily available copies of my tickets has made my trip easier on multiple occasions.