I think people often hear 'bioelectric' and think it means electricity (electron flux) but what Levin's work is about is a pattern of voltage gradients (that cells maintain using electrically-non-neutral chemicals) that stores a pattern like a memory (or "target in morphospace" as Levin would say) of what to grow back into when the tissue is damaged.

It is about ion transfer between cells that sets up and maintains those patterns of electrochemical gradients. Gap junctions (the cellular pores that facilitate ion transfer) are not unique to neuron cells either, and nor are they even unique to multicellular tissues! It is now thought that this type of intercellular communication evolved in single-celled microorganisms even before the advent of multicellularity (like in biofilms and in quorum-sensing such as what yeasts are known to employ).

I totally see what you're saying if you interpret this as electricity like electrons/electromagnetic-fields in a wire with power running through it, but that is really not what Levin's work is about at all.