Ah, you must not have read the book, so you might have expected it to be more like the Lord of the Rings. You see, The Hobbit, or There and Back Again, is a children's book, and it's self-consciously supposed to be the book Bilbo himself writes about his adventure within J.R.R. Tolkien's world, which Tolkien has "discovered" and "translated." Moreover, the book is full of songs. It is a musical, really. Being released in 1937, the same year as Disney's fairly tame first movie, you can see that musical fantasy was obviously the style of the time. Disney and Tolkien-verse naturally reinforced one another over the years, literally creating the fantasy genre as we know it today, including D&D, movies, video games, renaissance faires, etc, all post-World War II diversions that created the popular genre we know today.
So, it's not as if Peter Jackson just pulled "Disneyishness" straight out of his... imagination. In 1937, The Hobbit was more Disney than Disney.