I agree. I never, ever moved our heat lamp. I just left it on one side of the brooder and as they grew and feathered out more they just stayed further away from it. No big science there, and they were fully feathered by 5-6 weeks because of it I think!
Depends on the size of the brooder and whether the brooder has good ventilation or not. Those who have small brooders have to pay more attention or they could cook their chicks. I'd hate to see someone accidentally cook their babies in a plastic tub because they thought the chicks would be able to get away from the heat.
I know keeping the light stationary worked well for you, but, if I remember correctly, your girls were in a large coop with the red light. They had plenty of space to move away.
My girls did not have space to escape heat if I didn't move the lamp up as they grew. At one point, I checked my brooder and it was 110 degrees... scared the living daylights out of me! I hadn't taken into account that as the heat goes up in the house on a warm day, the heat under the lamp would, too... and my birds couldn't escape it.