Neurons are among the oldest cells evolutionarily speaking. If you go beyond small clusters of cells you need a way to get signals across your organism. Short distances? No problem but larger distances or more complex instuctions, or better timed reactions you need 'cable'. Enter the neuron.

So basically neurons developed into 'intelligence' from a 'need' to communicate internally. From this you can evolve stuff like bigger muscles, legs, arms. Brain.

So unless we discover intelligence in plants I'm afraid neurons are the only way to go.