In addition to everything else it must be justified energized work. It is not common when you can meet the requirements to justify energized work. However, there are provisions to permit troubleshooting on energized equipment.
Exactly what cannot be shutdown?
In the plant I spent a lot of time at, there was NO energized work, other than troubleshooting. They did have an energized work permit, and it required the signature of the plant electrical engineer and plant manager, but it was never used because the word from corporate was that if they signed that permit and something went wrong both of those persons would be fired.
There were a lot of projects where we did the preliminary work, and then waited months for an outage to complete the work. Even landing conductors for 120 volt controls was not permitted if the panel was energized.