Does having a central axon and dendrites result in any advantage compared to if the neuron was symmetrical?
Asymmetry to essential to neuronal function, particularly in the peripheral nervous system. This is because the dendrites of a neuron receive synaptic potentials, which are graded and decay with distance. Dendrites are typically short such that a synaptic potential is still above threshold by the time it reaches the axon hillock (sometimes called trigger zone), so that a subsequent action potential can fire. Axons need to be long (some are up to a meter long, in the leg) to transmit signals long distances in the body. To make a neuron symmetrical, one of these qualities would have to be compromised and neuronal function would suffer as a result.
Source: Principles of Neural Science, 5th ed (2012), Kandel et al. Chapters 1-6.