Wikipedia states that "sound symbolic words occur more often in Japanese than in English..." Indeed, Amazon.jp has a 4500-word dictionary just for these words. Is there any research or solid understanding of why Japanese is such a sound symbolic-rich language?
It is not 100 percent clear, but I will try to list up the many theories that have been established:
Japanese does not have as many verbs as other languages to express subtle nuances of an action. For example, in English, we can say daddle, waddle, trudge and toddle, whereas in Japanese, you would express these nuances with mimetic words like のろのろ、よたよた、とぼとぼ、よちよち and attach them to the verb 歩く (to walk).
They give much more vividness in expressing states, emotions, movements and so on as these symbolic words are used much more frequently in emotive and informal situations. For example, when you hit your hand against a table, you could use コンコン、トントン、ゴンゴン、or ドンドン, and they each represent a different sound and force on the table. In English, we can say "tap it softly" or "hit it hard", but that only represents the force and not the sound of the action.
Young children in Japan pick up and use sound symbolic words first. If you look at any book for young children, they are filled with sound symbolic words. As you may know, children learn language by hearing sounds and relating them to actions, emotions, etc. Because sound symbolic words are often related to visual and auditory sensual expressions, they are easily acquired naturally (this is the same reason they are difficult for second language learners, because they have less of an opportunity to relate sounds with real life events)
Japanese has deep connections with sounds and rhythm. It is a mora-based language and has natural patterns. You will notice that 4 mora is extremely common in Japanese, which is also reflected in its common use of sound symbolic words which are often 4 mora.
Natural sounds are pleasing and have an elegance to them. 風流 is a highly regarded notion in Japan, and natural sounds are known to have 風流. Also, being in harmony with nature is a highly regarded concept, and expressing oneself using sounds which mimic sounds from nature would be the most "natural" thing to do.