What is the advantage to neurons being asymmetrical?
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.