In case of emergency, drones just land where they are, or they could try to go back to the point of origin. Depending on the emergency, the drone might lose connection with the operator, in which case your own location is not very useful. I didn't run into emergencies lately but usually as far as I know the operator sets out to retrieve the drone.
> Wondering if GPS on the drone would dramatically affect battery life as well?
The vast majority of consumer drones already have GPS (on the device) today.
> have also used a drone to follow me while on a bicycle or in a car
It's more likely the drone follows you with computer vision although GPS could potentially help if the drone completely loses you. I imagine your phone location will be more helpful in pointing out the general direction than actually getting you in the center of the shot. It's not that accurate, and there are more variables at play like the vertical angle.