Why would running the coil cable straight for ~10 inches affect metal detector sensitivity?
It isn't really a question of sensitivity per se, but rather an issue relating to whether the connecting cable interacts with the coil and detunes it or reduces its Q.

Two wires interact magnetically if they are parallel and close to each other. Separating them or changing the angle reduces their interaction, and if they're perpendicular, there's no interaction at any distance.

Therefore, if you run the cable along any straight path that intersects the axis of the coil, you'll minimize any adverse effects it might have on the operation of the coil. By the time you're at least 10" away (probably determined empirically), any possible effects from wrapping the cable are too small to matter.