Why does the nerve action potential needs potassium?
The action potential is mediated by the opening of Na+ channels, which happens in the order of milliseconds (e.g., Aldrich &amp; Stevens (1987)). Repolarization occurs through the opening of K+channels. Their opening is delayed by a few milliseconds (Purves et al., 2001) to allow Na+ to pour into the cell through Na+ channels. After that delay, the opening of K+ channels occurs also in the order of milliseconds. After these two processes are over, the membrane enters a refractory period, again on a millisecond scale. Then the membrane is ready for another action potential.

The Na+,K+-ATPase, on the other hand, has nothing to do in the action potential process as such. It operates much more sluggishly and it can by no means keep up with the rapid channel gating during action potentials. Instead, the Na+,K+-ATPase activity operates at the background to maintain the overall ion homeostasis. As an analogy, the power adapter of a laptop PC can never keep up with the processor speeds; instead, it functions in the background keeping the battery charged.

Then why two different ions? Because two different species of ions are necessary because they fulfill opposite roles in terms of polarization and reploarization.

References
- Aldrich &amp; Stevens, J Neurosci (1987); 7(2): 418-31
- Purves et al., Reconstruction of the Action Potential. In: Neuroscience, 2nd ed. Sunderland (MA): Sinauer Associates (2001)