The ball is a sideslip indicator on a symmetrical aircraft only
In the helicopter axes (where the ball is actually installed) aerodynamic forces are balanced by inertia forces. The ball only sees inertia forces, but they are a view of the opposing aerodynamic forces.
A centered ball indicates that there is no inertia sideforce, and therefore no aerodynamic sideforce. On a symmetrical airplane, the sideforce only comes with sideslip. Flying with a zero centered ball guarantees flying with zero sideslip.
When the airplane is no longer symmetrical, a twin engine aircraft with an engine failure fo example, there is no such obvious link. The remaining engine provides a yawing moment that has to be counterbalanced by a lateral force on the rudder. Flying with zero sideslip means no aerodynamic sideforce on the fuselage. The resulting aerodynamic sideforce is the rudder force and is not zero. It has thus to be compensated by a lateral inertia force and the ball is not centered. Flying with a centered ball means that there is no lateral aerodynamic force. The rudder sideforce needs to be compensated by a fuselage aerodynamic sideforce that can only come from a sideslip angle.
The classical single rotor helicopter is not symmetrical. In zero sideslip conditions (no aerodynamic fuselage sideforce) there is still a lateral aerodynamic sideforce coming from the tail rotor thrust. The ball is therefore not centered. A centered ball means that there is some sideslip, inducing a fuselage lateral sideforce opposing the tail rotor thust.
In high speed conditions a small sideslip angle can generate a significant fuselage side force. The sideslip angle with a centered ball is therefore limited. In low speed conditions a much larger sideslip angle is needed. Close to hover there is not enough speed to compensate for the (high) tail rotor thrust and it is no longer possible to fly with a centered ball.
Using the string in low speed conditions and the ball in the high speed range makes sense.