Wire stiffness controls the rate of tooth movement, but:
Rapid tooth movement may be painful
May be difficult to engage stiff wires with brackets in grossly misaligned dentitions
May lead to bracket debonding
So, treatment usually involves a series of wires:
Initially use low stiffness wires to move large distances, slowly
Wires replaced with increasingly stiff ones as treatment progresses
Higher stiffness leads to quicker movement, smaller distances involved