For a neuron to function, an input of free energy from ATP is required to set up the sodium and potassium ion concentration gradients such that a signal can be propagated down the axon of a neuron without the necessity of ATP. The system could have worked the opposite way. The neuron could have used ATP to move ions across when a signal was being propagated and then allow natural diffusion to return the ions to their respective sides of the membrane. What advantage does the organism have using ATP up front

The lack of ATP would slow nerve responses to generate an action potential

Explanation:

Adenosine triphosphate (ATP) is the main source of energy in the cells. Moreover, ATPases are pumps that use ATP in order to transport sodium and potassium ions across the cell membrane and thus create an action potential. In stressful situations (e.g., escape from a predator) the lack of ATP would not allow to develop fast nerve responses, thereby ATP is required during rest periods and the flow of ions is used when is required a fast response.