Why is active transport needed in repolarization?

Question

During the repolarization phase of an action potential, the potassium ions diffuse out of the cell, and active transport begins.

What I do not understand is why active transport is needed when the movement of ions is not against their concentration gradient?

Since the potassium ions have diffused out in repolarization, only the sodium ions are left in the intracellular space.

The sodium/potassium pump is used to pump 3 sodium ions out and 2 potassium ions in. However, isn't there a concentration gradient as the sodium ions are moving out of the cell, where there are no sodium ions, and thus from a high concentration to a low concentration?

Is it because the active transport allows the imbalance to occur (3 out and 2 in)?

Answer 1

...when the movement of ions is not against their concentration gradient...

This assumption is incorrect: Na⁺ has to be pumped out of the cell against its chemical gradient (table 1) and against its electrical gradient, given that the inside of the cell is negative (Fig. 1).

...potassium ions have diffused out in repolarization, only the sodium ions are left in the intracellular space

This is incorrect: There are heaps of K⁺ ions in the cell, also after repolarization. A tiny fraction exits the cell during repolarization.

...moving out of the cell where there are no sodium ions...

This is incorrect; there are Na⁺ ions out of the cell, heaps in fact. You should be aware that the flux of ions is not an all-or-nothing phenomenon. It is a flux of relatively few ions out of a pool of them. Action potential formation and ion gradients are membrane-bound phenomena. While Na⁺ may enter the cell during an action potential, there is still a nearly infinite large amount of Na⁺ left in the intercellular space.

^{Table 1. approximate ion concentrations in and out of the cell. source: Med Quarterly}

^{Fig. 1. Action potential. source: UC Davis}