The desk is in the wrong place
Look at where the production desk usually is. Back of the room, often behind everyone, sometimes in a booth with a window, occasionally in a different room entirely.
That position was chosen for the equipment... power, cables, somewhere it does not block a sightline. It was not chosen for the person.
And the person running lyrics has a job that is almost entirely about watching the platform. When the leader signals a repeat. When the speaker moves on. When a song ends earlier than planned. All of that information is at the front, and the operator is at the back, frequently at an angle where they can see the screen or the platform but not both.
What a handheld changes
If advancing the plan can happen from a phone, the operator can stand where the information is.
Beside the platform. At the side of the room. Somewhere with a clear view of both the leader and the screen. They are still operating; they are just doing it from a position where they can see what they are responding to.
The actions are the ones that make up most of a service: move to the next item, step through lines, jump to a section, go back. Swipe and tap.
Who this is actually for
The person who cannot see from the desk. The most common case. A booth with a bad angle, a pillar, a room shape that puts the platform out of view. Rather than solving it with a camera pointed at the stage and a monitor, the operator can simply move.
Someone who is also doing something else. A musician who advances slides between playing. A person who leads and operates. A phone in a pocket works there; a desk does not.
A team of two who need to swap. One at the desk on cameras, one handheld on the plan, standing where they can see. Two people, two positions, both useful.
Someone intimidated by the desk. Worth naming: a desk covered in controls is a barrier for a new volunteer. Handing them a phone and saying "swipe when the song moves on" is a much smaller ask, and it is a real first job.
What it does not replace
Being clear, because a handheld is not a whole production system.
It advances a prepared plan. It does not build one, does not manage cameras well, is not a place to fix a problem, and is not where you want to be when something goes wrong.
The desk is still the desk. The handheld is a remote for the most repetitive part of the job... the part that is mostly "keep up with the room" and barely needs a keyboard at all.
Which is exactly why it works: that part is most of a service, by time. An hour of a two-hour event is someone advancing through prepared material in response to what the room does.
Practical notes
Prepare the plan properly beforehand. This only works if the order is right. Fixing a plan on a phone mid-service is unpleasant; you want a desk for that.
Screen brightness down, notifications off. Same discipline as any device on or near a platform.
Decide who is authoritative. If someone is at the desk and someone has the phone, agree who advances. Two people advancing is worse than either alone.
Keep the desk running. The handheld is a remote, not a replacement. If it disconnects, the desk still works... verify that before relying on it.
Charge it. Recurring theme, and it keeps happening.
The general point
There is an assumption baked into most production tooling: the operator sits at a station, facing screens.
That assumption comes from broadcast facilities, where it is correct... a control room is a room designed around the operator, with everything they need in front of them.
A small venue does not have a control room. It has a table where the cables reach. The operator's position was determined by electrical convenience, and then everything else was designed as though it had been chosen for visibility.
I spent about twenty years sitting at whichever table the cables reached, which is where this one came from. Letting the repetitive part of the job leave the desk is a small correction to that. The operator goes where the information is, instead of the information having to be piped to where the operator was put.