With regard to your last point, I'm not saying a reader would necessarily have to use a character list. In other words, it isn't physically impossible to read the books without it. But not every reader reads the books back-to-back, and not every reader has a good memory. Consequently, I wouldn't go so far as to say that a series is flawed if some readers would benefit from a character list. It's typically a convenience, not a necessity. Anyway, flaws, like everything else, are to some extent a matter of taste. The kind of series you're talking about, where the MC is more or less completely static, might also be considered flawed by some people, though I think most readers have enjoyed that kind of book from time to time.
I'm sure the way books are labeled is often for perceived marketing advantage. However, if we're speaking in terms of literary analysis rather than marketing, that's precisely why I would argue that everything publishers call a series may not be a true series. I'd be the first to admit that's merely my own opinion. I think lumping a whole bunch of book groupings together, some of which are very tightly integrated, and some of which are so loosely integrated that only MC and genre unite them, isn't really useful, and the fact that the labeling isn't consistent makes it even less useful.
We consider the concept of TV series as in some way analogous. There are series that do not have to be watched in a a specific order. Typically those are genre-linked anthologies--but those are usually called anthology series or something like that. I've also seen some of the mystery series that could probably be watched out of order, but even many of them benefit from sequential viewing. Not so long ago, I was having difficulty figuring out the relationships between the characters in an Australian series. Everything became clear when I realized that I'd picked up season 2 by accident when I meant to start with season 1.
When
Magnum PI first aired, I watched it with great pleasure, and recently I tried rewatching it. It's somewhere between action and mystery, probably closer to action most of the time, and the shows can be watched out of order. But that's precisely why I didn't like at as well viewing it decades late. Certain elements, like the Magnum-Higgins relationship, are basically static. They fluctuate from time to time, but usually end up back more or less in the same place, which is one of things that makes them less believable. People do change. Relationships do change.
Of course, if a writer is focusing on something like the intricacies of solving a crime rather than on personal relationships, it makes sense the writing could be less sequential. But in anything that's more character-focused, it would seem much harder to pull that off. Sadly, I haven't read the Rabbit Quartet, but I did take a quick look at some of the commentary, and, though one may not need to read the books in order to understand the MCs, it certainly seems as if it would be better to read them in order to get the full impact of Updike's social commentary. In any case, there's a clear chronological progression. I have a hard time imagining a reader deliberately reading them out of order, even if they are understandable that way.
As with so many other things, to each his own.
