One of the reasons I still use paper is that, it's easier to get the item out of your pocket and show it to the person answering.
The current generation of people asking to see your pass have grown up with paper and started their current job looking at printed boarding passes. Some have already had to adapt from the flimsy carbon coupon to the ATB ticket and then to home printed A4 on dodgy ink jet with the page 2/3 full of advertising and now have to adapt again. So they are not always quick at recognising where on the screen to look for the information. Lastly, the information on the screen may be shown small, so as to give maximum space to the QR code.
I print my home receipts on a laser (or a high quality inkjet if the colour is crtical) on a 250 gram card that is not dissimilar in look and feel to an ATB - but is the same size. Although setting up the margins to get the best result took a few tries (each carrier formats the A4 page differently
) it's now very easy and I get a boarding pass that is not flimsy, is easy to read
and has the QR code.