I would agree with your appreciation of Miike's films as often being less interesting for their, often standard, plots than their "scenes, ideas, characters or moods that he creates" that often move into interesting and idiosyncratic areas. The weird 'regression into childhood' that happens to one of the bad guys at the end of Andromedia for example is an interesting take on the cyberspace film trend of the mid-90s. A film that I like a lot is Full Metal Yakuza which takes a really goofy premise (rather cowardly yakuza wannabe with an idol complex about his gang boss ends up getting shot to pieces as well when the boss is assassinated and then gets patchworked back together with parts of his boss cyborg-style (by Tomoro Taguchi from the Tetsuo films!) before going on a roaring rampage of revenge) and makes it surprisingly interesting, both fun, disturbing and surprisingly moving at times! As well as riffing on the standard yakuza film template (and notions of masculinity and idol worship that are very similar to Gozu) in amusing ways.
Takashi Miike does seem to be in that vein of 'studio system without a studio' directors who seem to want to be constantly working on films and working with pre-existing material to mould a film out of (remakes, anime and computer game adaptations, yakuza films, even One Missed Call at the height of the Asian horror trend kicked off by Ring and Ju-On!) rather than cultivating particular passion projects, though he seems a bit less prolific in recent years compared to when he had the potential to make many films in quick succession for the straight to video market in the 1990s and early 2000s (I suppose we have not got 'straight to internet' films yet to fill that niche! Or rather I suppose that the area has gone 'prestige' instead with Netflix et al!). Its one of the reasons why, having enjoyed previous work, I would probably be curious to see any "Takashi Miike" film over the content of a particular film itself. Even Ninja Kids!!! (though that might be pushing it! I'd be more likely to pull Jellyfish Eyes out of my kevyip first before tracking that one down!)
I like that Jess Franco seemed to have the model of finding sympathetic patron producers (who defined particular periods of his career, with more or less money involved), and even in the decline into straight to video, straight up sex films and eventually into almost private 'home movies' shot in and around his house, seemed to retain that distinctively unique 'Franco-ness', even if the films never reached any kind of audience. (Kind of the same trajectory as Ken Russell in some ways, though of course Russell hit higher heights!)
I have always found it interesting that this kind of director is almost existing outside of a need to have their work seen and assessed by an audience at all. Presumably as long as they are providing the required or expected elements that the financiers are looking for (and the content that audiences will pay to see), there is a bit of leeway to then do their own thing with the general story or tone of the film. They really seem like the type of director that the auteur theory seems to most benefit, as that approach allows for an easy highlighting of particular themes (or camera framing, length of shots, locations, favourite actors, etc) in otherwise disparate works by suggesting a certain guiding sensibility (Though of course the danger of total adherence to the auteur theory is that it has the potential to turn the accidental and haphazard nature of filmmaking into a career that appears to have been pre-planned and carefully mapped out from the very start. Though the best work through the auteur perspective often tries to show the vicissitudes of fate even on the greatest directors: Orson Welles being the prime example!)
I guess we could add Woody Allen into that area of a prolific, 'industrial' director who is almost creating entirely to keep themselves working at this point (even Clint Eastwood, though he does have old-school studio patronage with Warners), at least until recent events, though Allen has a narrower range of film that he appears able to make (narrower even than Eastwood, who has been more experimental than ever in recent years with historical dramas, musicals, true story films, and so on), despite the couple of attempts at doing musicals. You probably would never see Allen doing a gangster film, to kids film, to horror, to sci-fi, to opera adaptation, etc in such a short space of time!