By pass hose

That little hose does more than just bypass the thermostat. The ends are 2 different sizes to create a mechanical differential. This is required for a impellertype pump to pull from one direction and push in the other.
I don't know squat about the electric water pumps. If they are some other design inside such as a vein pump, like a power steering pump, they wouldn't need the flow restriction / mechanical differential.