It seems like a borderline category mistake to claim that because the components of some system have property P then that system is somehow better fitted to have property P itself. There are exceptions (like P="reliability", or P="speed", thinking of transistors in a chip, perhaps) but in general, it doesn't seem to follow. Few transistors have Turing completeness, for example, but could be components of a system possessing that property. I don't see prima face why Agency should belong to the class of properties that transfer upwards from component to composed system.
Anthropomorphizing neurons by ascribing "selfishness", "adventurousness", and so on to them seems to compound this error in an effort to persuade. I doubt Dennett intends this in the excerpted quote.
Anyway, the "heterarchy of agents" view of mind doesn't need personality-endowed neurons, and has some compelling features which are explained pretty well in the article.
Regards "level 4, the self", though, I wonder how well evidenced a "prime-ministerial agent" type of self is. The article seems to take that on faith versus alternate models such as a set of competing high-level agents that compete or cooperate to occupy the driver's seat. Equating this with abnormal states of affairs like schizophrenia or demonic possession seems a bit facile.. (even disregarding the implied antique three-faces-of-Eve view of schizophrenia.)
Just because there aren't gross changes in behaviour or mentation, how would you know that a single top-level agent is consistently running the show? We're all familiar with mood-swings and role strain, but our strongly held belief in a ruling self makes us attribute these to other factors than agent swap-out. I think it's equally plausible that pathological multi-agency could be ascribed to abnormally divergent agents, rather than the mere existence of more than one top-level agent.
Maybe swapping top-level agents in and out is SOP, and a uniquely privileged Self should be treated with caution as a possible metaphysical fiction.