My personal view on it is (likely) as far from making logos as it is from telling stories. That is at least one but maybe multiple paradigms away.
Im quite confident that something like dall-e and various next-gen clip models together with more controlled user inputs such as make this eye smaller or I want an eye here, a mouth here and add a proper way to render vectors with color choices it would be possible to get a result that would need very little polishing. We did this back ion january/feb when clip and dall-e had only been out for a few weeks and that was the first real big sign that something like this would be possible.
Heres some more recent experiments i did last night with letting a model complete a design.