Nobody in any academic field takes Frazer seriously anymore, and the idea that there was a "Diana system" is overstating the case. In the areas where the Celts lived, for example, we have over 400 names of Gods and Goddesses, more than 300 of which occur only once in the historical record. In other words, people worshipped local Gods rather than wide-ranging ones. When the Romans described the area, however, they named any Goddess who remotely resembled Diana "Diana," which is why it appeared to scholars like Frazer as if Diana, Mars, Minerva, etc, were widely worshipped by ancient Celts. In fact, after the Romans moved in, they often added their own name to the Celtic name, and combined their mythology with the Celtic mythology, so we have Sulis Minerva, Mercury Artaios, etc. But this is certainly an artifact of Roman occupation, not a reflection of a wide-ranging cult of Diana (or anyone else) going back to before that occupation.

Stilly is certainly right that the importance of the oak goes back to before Classical times, in other words, before we have good descriptions of anyone's religion. This makes answering a "why" question impossible. The idea that the oak was so common is certainly a possibility, but isn't the rare item usually accorded special importance too?

The real question, it seems to me, is: is it really true that "the oak figures so much in folklore?" What examples of folklore do we have with oaks in them? What about other trees? Certainly in America, the pine features most heavily ("In the pines," "Piney woods," etc) In Ireland, Hazel and Yew seem to have been equally important as oak, and feature equally in folklore, so it depends where you go. I know of no study that actually compares the number of references to oaks versus those of other trees in the folklore of any region of the world, which would be a necessary precursor even to the claim that the oak figures particularly heavily in anyone's folklore.

It would certainly be accurate, however, to say that the oak figures heavily in commentaries on folklore by scholars interested in mythology and, especially, druidism; in other words, people like Frazer. Classical writers mentioned that the oak was particularly important to the Druids, and eighteenth century Druidic revivalists and other neopagans seized on this idea, making the oak central to their own belief systems. Meanwhile, Frazer's writings were in themselves widely influential. (The idea of the oak's importance to druids does not seem to have been universally true, by the way, but certainly in Britain, Gaul, and even Celtic Galatia we have some indications that it WAS true. In Ireland it's a different story).

By the way, "cult," when used by anthropologists and folklorists, does not necessarily have the negative connotations Stilly suggests. If we speak of a "cult of Diana" we mean beliefs about and worship of Diana especially, within a larger religion that also includes other aspects. Thus we also speak of the "cult of the Virgin Mary" within the Roman catholic religion. We don't mean people who program your kids to give all their money to the spiritual leader!