It's not just that computers were specifically designed for english speakers. It's that, even trying to specifically design for chinese speakers, it winds up clumsy to use. It doesn't matter the input method - big 4, pinyin, bopomofo - they're considerably clumsier than just typing out english or spanish or icelandish on a keyboard.

You may say that the problem is the small keyboard. But if you make the keyboard big enough, it takes three people to operate. (Literally - I have seen such a keyboard, for Kanji. It was huge. One person couldn't run it, because some of the shift keys were not within arm's reach of the keys they shifted.) So that's not an answer for most people.

Ideograph-based languages are clumsier to type than alphabet-based languages. They just are, and there is no great solution. The very information density that you keep harping on works against them in this respect.

Hmm I seem to be misinformed. I totally forgot to think about pinyin. Apparently it's as fast or faster than english. For example, hitting "jtkqwrhyz" on your keyboard will give you "Jin-tian kong-qi wu-ran hen yan-zhong" which translates to "The air pollution is pretty severe today". I don't type in pinyin though.