I guess it depends what you are trying to achieve by cooking an omelette. Taking the analogy to an extreme:
If you want to serve a really high-quality meal and are willing to wait a few days or weeks to get the omelette then you would probably wait for a chef from the omelette department, or hire in an external consulting chef. Note that a single omelette will take a long time to get this way, as you will probably also have to get authorisation to hire/spend money/use another teams resources.
If you needed food now, and if eggs in a pan now are better than omelettes in a few weeks, you would probably just find someone from your team to do it and you would have an omelette within the hour. It won't be as good, but it's better than waiting if you are hungry.
If you weren't cooking an omelette, and were writing a report trying to assess if the omelette team should be rolled into the frittata, you probably wouldn't ask the omelette team to write this report. Sure, they might have the most knowledge of how the team works and their capabilities, but asking the omelette team to write this report might have a pro-omelette bias because there is a conflict-of-interest in terms of job preservation.