Firstly, as was noted in the comments (by Tsuyoshi Ito), that the same thing cannot be done with other adjectives ending in ～らか.

On the other hand, there exists a number of adjectives, which can function both as イ-adjective and as ナ-adjective, e.g.

大きい   大きな
小さい   小さな
真っ白い 真っ白な (etc.)
細かい   細かな
暖かい   暖かな
四角い   四角な (etc.)
柔らかい 柔らかな

(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 やわらかい and 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 やわらかいお餅 and 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, whereas やわらかな suggests a subjective experience of softness/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.

Firstly, as was noted in the comments (by Tsuyoshi Ito), that the same thing cannot be done with other adjectives ending in ～らか.

On the other hand, there exists a number of adjectives, which can function both as イ-adjective and as ナ-adjective, e.g.

大きい   大きな
小さい   小さな
真っ白い 真っ白な (etc.)
細かい   細かな
暖かい   暖かな
四角い   四角な (etc.)
柔らかい 柔らかな

(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 やわらかい and 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 やわらかいお餅 and 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.

Firstly, as was noted in the comments (by Tsuyoshi Ito), that the same thing cannot be done with other adjectives ending in ～らか.

On the other hand, there exists a number of adjectives, which can function both as イ-adjective and as ナ-adjective, e.g.

大きい   大きな
小さい   小さな
真っ白い 真っ白な (etc.)
細かい   細かな
暖かい   暖かな
四角い   四角な (etc.)
柔らかい 柔らかな

(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 やわらかい and 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 やわらかいお餅 and 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, whereas やわらかな suggests a subjective experience of softness/gentleness.

But even if this is the case, not every Japanese person seems to perceive these subtleties in the same way...

Firstly, as was noted in the comments (by Tsuyoshi Ito), that the same thing cannot be done with other adjectives ending in ～らか.

On the other hand, there exists a number of adjectives, which can function both as イ-adjective and as ナ-adjective, e.g.

大きい   大きな
小さい   小さな
真っ白い 真っ白な (etc.)
細かい   細かな
暖かい   暖かな
四角い   四角な (etc.)
柔らかい 柔らかな

(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 やわらかい and 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 やわらかいお餅 and 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, whereas やわらかな suggests a subjective experience of softness/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.