The coinage of new words and phrases into English has been greatly enhanced by the pleasure we get from playing with words. There are numerous alliterative and rhyming idioms, which are a significant feature of the language. These aren't restricted to poets and Cockneys; everyone uses them. We start in the nursery with choo-choos, move on in adult life to hanky-panky and end up in the nursing home having a sing-song.
The repeating of parts of words to make new forms is called reduplication. There are various categories of this: rhyming, exact and ablaut (vowel substitution). Examples, are respectively, okey-dokey, wee-wee and zig-zag. The impetus for the coining of these seems to be nothing more than the enjoyment of wordplay. The words that make up these reduplicated idioms often have little meaning in themselves and only appear as part of a pair. In other cases, one word will allude to some existing meaning and the other half of the pair is added for effect or emphasis.
New coinages have often appeared at times of national confidence, when an outgoing and playful nature is expressed in language; for example, during the 1920s, following the First World War, when many nonsense word pairs were coined - the bee's knees, heebie-jeebies etc. That said, the introduction of such terms begin with Old English and continues today. Willy-nilly is over a thousand years old. Riff-raff dates from the 1400s and helter-skelter, arsy-versy (a form of vice-versa), and hocus-pocus all date from the 16th century. Coming up to date we have bling-bling, boob-tube and hip-hop. I've not yet recorded a 21st century reduplication. Bling-bling comes very close but is 20th century. 'Bieber Fever' is certainly 21st century, but isn't quite a reduplication.
Here are a few examples, there are many more:
Rhyming: - These are reminiscent of Cockney rhyming slang, although in that the rhyme is usually with some other unspoken word, which doesn't form part of the phrase; for example, trouble and strife - wife. There are a few exceptions to this guideline, for example, chevy chase - face.
Ablaut: - These are phrases suggestive of a toing and froing motion, that is, indicating a thing that is this and then that; for example, ding-dong, see-saw, tick-tock, zig-zag. Almost all of these use the vowel 'i' in the first part of the reduplication and either 'a' or 'o' in the second part. Why? I don't know.