What, Why dual power supply?
I think you are trying to view voltages as absolutes, the root of the negative voltage is the ground or the voltage reference. That is the place where you agree that the voltage is 0V we mostly interpret voltages as differences of potential, so as an exercise let's take your circuit and say that ground is not 0V but 20V so Vs is 29 and -Vs is 11. The difference of potential in both cases is 9 volts but relative to what reference is what decides the sign. If you make the gnd -9V then the voltage that was "negative" just becomes 0.

There is no change in what happens during electron flow, they will move from lower potential to higher potential as always(in most circuit books they write the current as going from high to low, but they are assuming protons move in this case, electron current is always the opposite direction)

you asked for a practical usage, the most practical one is that I can use one voltage(positive) to make it spin one way and negative to make it spin in the opposite direction. This is because I changed the direction of the current, but physically the same thing is happening, electrons are following the same rule.

remember that the ground being 0V is a convention we use for simplicity and this allows us to represent most voltages as a single number. However, a voltage is always a difference between two points and one doesn't always have to be 0.

To stop talking about voltages, you can just use height, let's say I am 6 feet tall and you are 7 feet tall, the difference is 1 feet either way, but if I use the smaller as the reference it is -1 and if I use the maximum as a reference it is 1.