Many many years ago I read a book called "El camino del Tao", from Alan Watts (I guess the English version must be, "Tao: The Watercourse Way"). In it, Watts explained exactly the same idea, how chinese characters evolved from simple drawings that became more and more abstract. While most non-Asians would say that chinese characters are unintelligible, one of our most fundamental habilities actually is that of visual recognition, and so Watts proposed that Chinese could be the written universal language just as English had become the spoken universal language, which actually makes a lot of sense. Take for example the following simple logogram, 女, it wouldn't matter how anyone would pronounce it (e.g. nǚ, onna, mujer, woman, Frau or femme), everyone would understand it!
Apart from the practical aspects behind logograms, one that becomes evident almost immediately is that of beauty, both in the characters themselves and in the ideas that can be expressed. One example I love is that of 花火 (hanabi, in Japanese), because translated into English (firework) or Spanish (fuego artificial), the word doesn't seem particularly significant, and so one has to understand it in Japanese: Flower of Fire (hana+hi); fascinating!