You're harnessing the entire energy output of a star. No need to transport anything - this is gathering, not hunting.
No, if we have a dyson sphere, we are everywhere playa
This metaphor doesn’t make sense to me.
I'm guessing it's more like making a living space in the sphere itself or somewhere nearby and using the energy there (maybe exporting some percentage to Earth).
Because if we're able to build the sphere itself, we probably would already know some way to cool it down in space so it doesn't burn itself, wasting all the money that went to its construction.