It's also something that started out as a very minor feature and grew over the editions - as you say, for the sake of uniqueness.
Taking on the form of beasts really belongs in shamanism. How shamanic the original druid belief system was we really don't know, since most of what we have comes from Roman historians, who wrote what they did (only
one person in that wicker man, Lord Summerisle?!), rather than what they believed.
Merlin does quite a lot of shapeshifting in T.H. White's books, and the movie version probably had an influence on D&D.