Why does zinc metal not deposit on copper from a zinc(II) ion solution without added electricity?

The premise that zinc metal does not deposit on copper from a zinc(II) ion solution is correct because the reaction is not spontaneous in that direction.

In electrochemistry, the spontaneity of a reaction is determined by its electromotive series potential. The reaction where zinc metal deposits from a zinc(II) ion solution onto copper metal is represented by the equation:

$$\text{Cu}+{\text{Zn}}^{2+}\to {\text{Cu}}^{2+}+\text{Zn}$$

This specific reaction has a potential of -1.10 volts. Because the potential is negative, the reaction does not proceed spontaneously from left to right under standard conditions. Instead, the spontaneous reaction is the reverse: metallic zinc dissolves in a solution of copper(II) ions to form metallic copper and zinc(II) ions, which yields a positive potential of +1.10 volts.12

Without an external source of electricity to drive the non-spontaneous direction, the system remains at equilibrium or favors the spontaneous oxidation of zinc metal by copper(II) ions.2