OK, now you've got me started. I've been living in Japan for the last three years, and, since my goal is Japanese fluencey, I've spend an enormous amount of time studying kanji.
Although there is an economy of expression (one character words) I still think Kanji suffers from a lack of word attack possibilities inherent in a phoneme based language. Once Westerners learn the Alphabet, and some basic phonics skills, we can take a stab at pronouncing any written word. There IS a Kanji dictionary, but it is based up the number of brush strokes in the word... quite the penmanship based way to try to look something up! I really think in the long run (a thousand years or so) a phoneme/alphabet based language will become dominant--it might still be Japanese, but words written like these, not pictographs.
Who knows what's going to happen in a thousand years. Look at the previous thousand. But I don't think Japanese people feel they are at any kind of disadvantage with having to learn kanji. I'm sure they hate it at the time (I know I do), but believe it or not, there are advantages. One/two characters per word, as you mentioned. Also, the meanings of those characters are very specific and allow for very specific words to be created or made up on the fly. For example they have one word that means "visiting a grave" and "the first fruit of spring." In my Japanese lesson I was confused by a sentence written all in kana until the teacher wrote the kanji for me. Also, there are so many words that sound the same in Japanese, that Japanese TV shows often have Japanese subtitles! When they read English they can't believe that we put up with so many strange spellings and have such ridiculously long words as "automobile."
I think the effect of computers will be interesting. People no longer have to write the things out, so they forget all those little strokes. They can read them, but writing ability is fading. Like us with spellcheckers.
So how do you like Okinawa? My wife and I honeymooned there. Let me know if you get up Tokyo way!