The best drag handle is the foreleg of the deer being dragged. Cut it off at the knee and tie both ends of it to a line around the deer's neck. It is padded, just right size, comfortable in the hand and is always there when needed, no need to carry a "drag handle." Grip it in the middle between the tie lines coming off of each end.
An improvement not shown in the photo is to allow just enough slack to loop a half hitch of both tie lines over the deer's nose. It is an easier streamlined drag with nothing flopping if you drag from the deer's nose. As Pete E said, short drag lines allow you to lift, which is needed if you drag over down logs or rough ground.
I don't drag unless it is clean ground downhill to a road or location that has some advantage over cutting it up or boning it out on the spot.