There's a couple of questions here. We'll unpack them one at a time.
Should the Story-ID question be closed?
I'm going to say no. The book series is certainly arguably on-topic (see below) which to my mind is sufficient to keep the question alive. It's well received and I can't see that there would be any benefit to removing it.
Should The Clan of the Cave Bear (and related works) be considered on-topic for future questions?
That would be a fairly firm 'no'. The book series is largely a work of historical fiction although, as Auel herself notes in various interviews, that while the story could be considered fantasy, or even science fiction, by its setting (note the total absence of any other fantastical elements), she would ideally prefer that it be categorised as a form of historical fiction which she coins 'prehistorical fiction', although if offered the forced choice, she'd probably push toward science fiction rather than fantasy because her work is based on scientific research.
That being said, as mentioned in Buzz's answer, in the first couple of books there was some early-installment weirdness involving the flatheads possessing groupthink telepathy as well as an incident where the main character mentally time travels to the 20th century. Although these would certainly be classed as on-topic incidents, they were retconned out of future books and never mentioned again. One or two very mild sci-fi elements in a book series spanning more than 17,000 pages of text would, to my mind, fall under our existing policy (Are works that aren't SF per se, but have occasional SFnal elements on-topic?), in the sense that questions about those elements would be on-topic, but questions about the book series in general wouldn't.
Q9: Do you see your work as Fantasy or something else?
A9: Though my books are written from a historical perspective, I have gone so far back that I am in the realm of prehistorical speculation rather than simple historical fact to weave my stories around. I think of my books as mainstream and that's were most people who read them look for them in book stores. I sometimes call them prehistoric fiction, but there is no category called "Prehistoric Fiction" in most stores. I have been a reader of Science Fiction and Fantasy for a long time, since I was 11 or 12 I think, so I understand it and I'm not at all surprised that readers of the genre might enjoy my books.
Of the two, I would think of my work as closer to Science Fiction than Fantasy. Science Fiction is not just about the future of space ships travelling to other planets, it is fiction based on science and I am using science as my basis for my fiction, but it's the science of prehistory - palaeontology and archaeology - rather than astronomy or physics. Science Fiction also involves logical speculation, and since I have had to speculate a great deal to create my prehistoric world and the characters that inhabit it, that's another reason I would end to put it in SF if I had to pick one. I have heard Science Fiction and Fantasy referred to as the fiction of ideas, and I like that definition, but it's the mainstream public that chooses my books for the most part.
Similarly, the pressers and blurbs for the films and TV shows spawned from her works are effusive in their praise of the precision of her research. This isn't an alternative world or a parallel universe, it's a fictionalised version of our world.
(May 27, 2010—New York, NY) Jean M. Auel, whose novels about prehistoric life have won acclaim for their inspired storytelling, meticulous attention to detail, and historic accuracy, has written the highly anticipated sixth and final book in the mega-bestselling Earth’s Children® series.
PRESS RELEASE: THE LAND OF PAINTED CAVES BY JEAN M. AUEL TO BE PUBLISHED MARCH 29, 2011