How do We Fix Spelling?

...it can be argued, perhaps, if they wish, that it's a question of style and beauty in the language, and that to make new words and new parts of speech might destroy that. But they cannot argue that respelling the words would have anything to do with the style. There's no form of art form or literary form, with the sole exception of crossword puzzles, in which the spelling makes a bit of difference to the style. And even crossword puzzles can be made with a different spelling. And if it's not the English professors that do it, and if we give them two years and nothing happens--and please don't invent three ways of doing it, just one way, that everybody is used to---if we wait three years and nothng happens, then we'll ask the philologists and the linguists and so on because they know how to do it. Adid you know that they can write any language with an alphabet so that you can read how it sounds in another language when you hear it? That's really something. So they ought to be able to do it in English alone.

If we can write words with letters from the English alphabet to phonetically reproduce words in other languages, like Mandarin or ARabic, then why can we not rearrange the letters in our own words to phonetically match the way they sound when we speak them?