- No need to print/distribute physical tickets
- Check-ins via the app reduces the need for ground personnel
- They can push inflight menus, shopping items, promotions etc.
- Flight updates and other notifications can get pushed to your device
- Integration of loyalty systems like airmiles
- They get to track various user behaviors
E-tickets were introduced in the 1990s, and essentially all airlines were using them by 2008. They don't have anything to do with phones. Mobile boarding passes are a more recent development.
You want the crew to be fully in charge of security. If they think the plane should turn around, it turns around. In the long term it is way cheaper to eat those costs then to start a whole industry about litigation for events like these, probably causing everyone to buy additional insurance etc.
You definitely don't want to give any incentive to anyone to "overlook" possible problems.
Once amortized against successful journeys the overall cost per passenger isn't significant. When it is, that's when we start seeing liability moved to the instigator.