Classical action potentials are just one mechanism of INTRAcellular communication - You could think of it as a special case of signaling via chemical concentration, where the chemical is cations and the propagation is faster+more directed than diffusion. INTERcellular signaling is only rarely mediated directly by voltage. Also, action potentials are most "useful" for propagating a signal rapidly over a long distance - It kind of accelerates and error-corrects (= reverses diffusive broadening) voltage signals down a linear path. Action potentials are so well known mostly because they show up in stuff that's easy to observe (long motor neurons) and they're easy to quantify

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