Have yet to try to hand the gate agent my laptop screen to scan. Will try!

that doesn't help my main worry of the battery dying.

nightmare scenario: your flight is delayed on the runway, so you end up watching a bunch of videos and draining the device battery. once you land, you sprint to catch your connecting flight following the delay. but just as you get to the gate to board, your phone dies and you can't prove you have a ticket before they close the door.

The reliability of the printer versus the phone is not at discussion. The reason to go with paper tickets is that they have significantly better availability and partition tolerance than phone based tickets. Using a paper ticket requires that the ticket be available at an exact future moment in time (when you board). The hassle of potentially using multiple unreliable printers ahead of time to prepare the paper ticket is an engineering trade off in providing a system with excellent time of use properties.

In the event that your personal printer is not functioning, the airport has many publicly accessible printers for your ticket printing convenience.

Still use the same Brother laser AIO purchased in 2007, a printer in 2006 and a Canon around the same time. They all work perfectly, only the rubber rollers on the double sided ADF had to be replaced.

I don’t have any phones still working of that vintage.

Not a perfect comparison but the argument is dumb because the item at issue is the printed product not the printer.

If a printer is broken, you find that out much earlier, with time to address the fault before it becomes a crisis.

If someone is carrying their printer with them on their entire trip in order to print their boarding passes at the last possible second at the gate, that's... A different kind of problem.