> that current methods require typing a phonetic equivalent using an alien character set [ie. Latin] which is then translated back to the desired Japanese character set
FWIW, the common "flick" method on phones is done using the native hiragana characters which by a coincidence handily map onto a T9-style layout https://lpgen.line-scdn.net/mobile-guide/7037/images/169626/...
Keyboard sold in Japan have the corresponding kana on their keys so you can input using native characters, but it's generally "only used by old people" https://lh3.googleusercontent.com/proxy/WdEEFbM3kmER2rJReyr0...
So using latin characters isn't required per se, but on PCs it tends to be a choice.