What drove me crazy when I started to learn Japanese was that a Kanji characters can have so many different pronunciations. The most egregious example is 煙草, whose pronunciation is the really just tabacco(tabako, or タバコ). I knew the etymologies and the historical context on why Japanese evolved like that, but it's nonetheless hard for me to remember all the pronunciations, at least initially.

Also, I find that knowing Kanji is essential in appreciating part of Japanese culture. Take their addresses, for example: Kinukawa is really meaningless, but 鬼怒川 is such a amazing name. Similarly, Akihabara means little if all we know is the pronunciation, yet its Kanji 秋叶原 is such a beautiful and poetic name that invokes complex emotions.