Firstly, as was noted in the comments (by Tsuyoshi Ito), that the same thing cannot be done with other adjectives ending in
On the other hand, there exists a number of adjectives, which can function both as イ-adjective and as ナ-adjective, e.g.
真っ白い 真っ白な (etc.)
四角い 四角な (etc.)
(but, of course, やわらかい is the only one ending in
～らかい). An investigation of the differences here might deserve a separate question.
As for the difference in usage, I have talked to quite a few native speakers, who maintain that there is no substantial difference in meaning between
やわらかな, which is only a handful of anecdotal evidence. On the other hand, here is an article (blog post?) about the difference between
やわらかなお餅, where the author says something along the lines, that a
やわらかなお餅 has a more gentle feel to it (he says
「やわらかな」のほうが落ち着く感じがする). Which, too, is at best anecdotal evidence.
One can only guess that maybe he means that
やわらかい is a more objective statement about the physical properties of the
お餅 (softness), whereas
やわらかな suggests a subjective experience of softness, or rather gentleness.
But even if this is the case, not every Japanese person seems to perceive these subtleties in the same way...
P.S. I noticed that I haven't answered your question, regarding the history of the difference. I will delete my answer, if it isn't contributing anything to the problem of answering your question.