How did researchers before that explain what the neurons do if they believed they did not have action potentials? Did they believe communication was done solely through chemical messaging?
Somewhat related, there is a roughly inverse correlation between neuron count and "computational power per neuron", "older and simpler" critters' neurons are more likely to be "less specialized" and more likely to use hundreds of different chemicals for transmitting intercellular signals, while "newer and more advanced" critters' neurons are more likely to be "specialized" and use just one chemical for transmitting intercellular signals
Action potential are almost strictly INTRAcellular events (minor exception being ephaptic effects) that are converted in a surprisingly noisy way into presynaptic transmitter release and variable postsynaptic changes in conductances.
Action potential are a clever kludge necessitated by being big and having long axons and needing to act quickly.