Some pitfalls: The screens have to be big, with no glare. Each musician needs access to a scanner that can handle oversize pages. There needs to be a format that lets the musicians make edits and annotations on the fly.
The tech has to work perfectly. How many of us have been to meetings where something went wrong with the projector, or with PowerPoint?
To either earn a living or even be reasonably busy as an amateur, musicians have to handle a lot of last-minute work with multiple groups that all have varying levels of tech savvy. The bandleader just has to be in possession of the physical sheets, to be absolutely assured that they will work.
Here’s a typical month at Worcester, and bear in mind it doesn’t include the voluntaries at the start and end of each service (though the start will sometimes be improvised, at least in part): http://www.worcestercathedral.co.uk/media/October_Scheme_201...
Organists would have to figure out some other strategy, though, since they do use both feet frequently. Still, if there's a button to push somewhere on the organ, that'd be at least easier than flipping a physical page.
For organists, these days pipe organs are usually outfit with a sequencer that allows the organist to program a list of registration changes (the combination of pipes/stops used) ahead of time; the organist then advances through the sequence of registrations, by bumping a bumper pedal with the side of their foot, or by pushing a toe stud pedal. Sometimes there are multiple toe stud pedals, which either allow for jumping straight to a specific combination, or for using the closest one as the program advance.
But yeah, even a button press or screen swipe should be easy enough to be useful in all but the most extreme cases (and in those cases a combination of memorization and automatic turning (e.g. tied to a metronome) could help further).
https://www.youtube.com/watch?v=985lfzTs79Q
I don't know what software he uses or how the pages get turned (by the time spent?).