If the PI is suitable for such work environments, how can I prove/convince my team?
It is of course impossible for us to advise on that without details of a specific application and environment.
However that won't stop me making some general observations:
The Raspi is a consumer device. Like a smart phone or TV. It does not come with anything that people in the industrial world would recognize as industrial strength specifications. For example min and max operating and storage temperatures are not specified. Neither is any resistance to shock and vibration, moisture, humidity. Etc, etc. What about tolerance of extreme local EMI?
This is not insurmountable though. Many people have used Pi in industrial applications.
One might have to take some measures during the design of your project. SD card failure is common resulting in unbootable Pi, so consider adopting a read-only root file system. Power and other connections are physically fragile. consider making robust power connections and such. You might need to attend to physical enclosures and mountings to ensure the Pi is not killed by shock or vibration. Similarly for protection from moisture, dirt and all the crap one finds in factories.
Do your own testing. When I was involved in such things in house designed boards and assemblies were extensively tested in environmental chambers, temperature and humidity cycling. They were tested for resistance to shock and vibration in giant test rigs that would shake and drop them repeatedly. Such testing will need to be done formally enough and signed off to satisfy everyone. It helps to have a Quality Control department/team that everyone trusts who can sign off on the results.
It's not unknown for systems to crash out when electric welders are fired up nearby, test for that.
Depending on what you need this can be a lot of work.
Having said that, I have had a few Pi running 24/7 for a year now, in remote and harsh locations, where getting out to fix them should they fail is very expensive.
Memory in C++ is a leaky abstraction .