First of all let me tell youwhy we need unmyelinated neurons.
Conduction speed depends on axon diameter as well as myelination; myelinating very small axons is just a waste of space and energy because the speed is limited by the diameter. Not every action potential NEEDS to reach the CNS ASAP, anyway. A(delta) pain fibres transmit fast, sharp pain quite quickly, and so need to be myelinated. Unmyelinated C fibres transmit dull, long lasting pain, so there is no benefit to having them transmit quickly.
The oligodendrocytes makes these unmyelinated neurons by certain process for the above mentioned function.