It loses the ready access to the relatively deep history available due to spelling being nearly frozen since the rise of early modern English. Shakespeare, from circa 1600 is readable with only slight difficulty. In contrast, Chaucer, circa 1400 while recognizable, is a puzzle to decipher. This deep history also shows in etymological roots.

It's also completely impractical given the wide variety of very differently pronounced English dialects and accents. In other words, it requires massive pronunciation reform too. If that's on the table, why not alter everyone's pronunciation to fit the orthography...