Single long axon vs serial neurons
First, I must clarify that a nerve is not the same as a neuron. A nerve is a collection of axons (with each axon a part of an individual neuron) in the peripheral nervous system. Thus, when you mention “single long axon such as the sciatic nerve”, this is technically an incorrect phrase as the sciatic nerve is a collection of many long axons. If one of these axons is nonfunctional, this would not severely affect the function of the entire sciatic nerve. However, you are right that if the entire sciatic nerve is severed, then there would be serious consequences downstream. 

Second, the primary advantage of conduction velocity is less dependent on length and more dependent on presence and degree of myelination (directly proportional to fiber diameter) and presence of nodes of Ranvier. 

With regards to the content of your question, the advantage of length is exactly what one might think--- greater distance. The sciatic nerve is the longest nerve in the body in order for our nervous system to innervate as far as the tip of our toes. Having hundreds of side-by-side series of neurons compared to hundreds of side-by-side axons seems like a far less efficient system in a couple of ways in exactly the two ways you mention: energy and time. 

Energy: Having serial neurons would require an increase the number of neurons needed to transmit a message. Having more neurons requires more Na+, K+ and Na/K pumps and individual channels, requiring more energy. 

Time: Having serial neurons would also require an increase in the number of synapses between neurons— either electrical or chemical. If the synapses are chemical, then time is increased many-many fold. If the synapses are electrical, then time is slightly increased by 10-fold per synapse compared to chemical synapses, but this would still take more time compared to having a single axon with myelination and nodes of Ranvier which by about 100-fold faster than a single electrical synapse. 

In summary, having longer nerves made up of axons rather than serial neurons is beneficial by improving energy and time efficiency, which allows our bodies to effectively innervate structures farther away.

Ref: 


Regarding delay of conduction: Chemical v. Electrical/Gap  Ch 10 of Principles of Neuroscience- "Synaptic Integration in the Central Nervous System" (Siegelbaum,
Kandel, Yuste) 5th ed. McGraw-Hill Medical, c2013.
Regarding conduction velocity of myelinated versus nonmyelinated
cells


Regarding the ATPase absolute number increase in serial vs one long axon, I assume this will depend on the number of neurons in series. However, I read this paper, which says that increased length between each node of Ranvier has been physiologically associated with increased conduction velocity. This suggests fewer needed nodes, despite concentrated ATPases at these locations, and thus fewer ATPases. I haven't been able to find studies which compare ATPase concentration in the soma compared to nodes of Ranvier within axons. 

Regarding energy use in soma vs axon, mitochondria are not only made in the soma but are concentrated in pre- and post-synaptic membranes (and growth cones). The more of these structures there are (as in serial neurons), the more presumed mitochondria. See mitochondria and neuronal activity. 

Finally, my literature search could not find studies which showed longest possible energetically feasible length for myelinated or unmyelinated neurons.