An example I've seen is a dozen construction workers on a big job site whose phones push-to-talk goes to the speakerphones of everyone on their team. This functionality was big with Nextel phones/service in the early cellular era.

I used to work on another ruggedized Android smartphone that focused on large commercial deployments. We focused more on hospitals than industrial. The PTT feature was a big selling feature. It was really popular with nurses communicating with the rest of their team on the floor. Think of it like a walkie talkie you can easily integrate tons of other daily work tasks with. Instead of just talking to your team you could also pull up charts, check emails, etc all on one device. Built into the PTT was also a panic button to sound an alarm for an emergency. It's just a handy flexible tool and from my understanding our customers found different useful ways to apply it to their needs.

If it's like the extra button on my phone (Cat S61) you should be able to set it up to do whatever you like. I have mine set to toggle the flashlight on long press which is super convenient.

I can imagine it being used as a walkie-talkie replacement.

There's a physical button you can program -- you can use it for PTT, or to turn on the flashlight, open your to-do list, etc.