On the Food network they boil potatoes, but they poach carrots. They poach turkey, but they boil eggs. They sauté’ onions, but they fry eggs in the same pan. Likewise, they fry hash browns, but they sauté’ onions in the same pan before adding the potatoes.
I can go on for days.
Poaching in olive oil, butter, wine, etc would give a different flavor. I agree that water poached carrots would be just a slower way to cook carrots than boiling them.