The sum of all edge nodes exceed the power in the datacenter, but the peak power provided to you from the datacenter significantly exceed your edge node capabilities.

A single datacenter machine with state of the art GPUs serving LLM inference can be drawing in the tens of kilowatts, and you borrow a sizable portion for a moment when you run a prompt on the heavier models.

A phone that has to count individual watts, or a laptop that peaks on dual digit sustained draw, isn't remotely comparable, and the gap isn't one or two hardware features.