What is the purpose of the adrenal medulla?
I have found the answer to the purpose of the adrenal medulla to be flexibility. Just like regulation for example of gene expression or metabolism occurs on many levels with different speeds and permanences of their effects, signalling needs to be available both quick and short-lived, and slower but with more long-lasting effects. The adrenal medulla provides exactly that.

Sympathetic adrenergic neurons are quick, but as quickly as they release their neurotransmitter, the effect is only of short duration and adrenalin is quickly cleared from the target area. Rather than giving off short bursts of adrenalin, the medulla maintains a constant systemic level of it and in response to stimulation raises or lowers that level. This response takes more time as blood circulates much slower than neurons respond, but its effects last longer.