Why do neurons have only one axon?
Neurons generally have one axon, because of the way it sums potentials from its dendrites. Right at the axon hillock (the little area where the axon protrudes from the soma), all the potentials are summed together. Now, you have to consider that what is actually summed here is dependent on the shape of the neuron, potentials lose amplitude as they travel towards the axon hillock. If there were multiple axons protruding from different sites, they would send out different signals and compromise the computational integrity of the neuron.

Instead of having multiple axons, a neuron simply branches its axon with axon collaterals. This way, all post synaptic sites are receiving virtually the same message.