Having a mobile boarding pass also gives passengers greater control at both the security checkpoint and boarding gate.
At the security checkpoint, a Transportation Security Administration (TSA) agent will always need to inspect a paper boarding pass, often marking it with a pen. A mobile boarding pass only needs to be scanned, which flyers can do themselves by simply holding the phone over the scanner, with no need for the screener to physically hold the device.
I always keep control of my phone and scan it myself. Sometimes the scanner is passenger-facing and while on some occasions I've had to reach over the kiosk, TSA screeners are aware some passengers have that preference.
When boarding, the procedure for most is to give the printed boarding pass to the gate agent to scan. But with a mobile boarding pass, the agent will likely direct you to place your phone over or under the scanner yourself. Unless there is a problem with scanning the boarding pass, I've never had to give up control of my phone to the boarding agent.
If a flight requires the use of a paper boarding pass, I'll still insist on scanning myself to prevent unnecessary physical interaction.