Computer character codes descended directly from pre-computer codes, either teletype or punched card. The advantage holds back through printing to writing itself; having a small, fixed set of glyphs that can represent anything is just better.
I really wonder why Arabic has never gone back to printing. What we think of the Arabic "alphabet" is just it's cursive form. They have an alphabet that is basically just Syriac. Would have been easier to render on low bit displays. wouldn't have to deal with the word initial variants etc.
Japanese has (slightly) more homophones and favors monosyllabic Sino-Japanese in compound words. That makes it hard to depend entirely on phonetic script. Same reason why English retains irregular spellings to help with some disambiguation.
