Yet <づ> and <ず> are phonetically indistinct but entered differently; the input scheme is really not based upon phonetics but on structure.
> It's also worth noting that from an English perspective the sound you associate with <ti> might be different from the sound a Japanese person might associate with it. Just because the usage isn't strictly the English phonetics, doesn't mean the symbols aren't being used phonetically.
I think you might confuse the words “phonetic” and “phonemic” here. One can argue that <づ> and <ず> are phonemically distinct in modern Japanese but certainly not phonetically, but <お> and <を> are certainly phonemically indistinct and <おう>, <オー> and <おお> are all phonemically and phonetically indistinct as well but entered differently.
More modern linguistic analyses also analyse the sound of <ち> as /ci/ in modern Japanese, due to the almost universal distinction made with <ティ> in modern Japanese, arguing that the historical /t/ has now split in /t/ and /c/, yet /ci/ is entered as <ti> and /ti/ as <thi>, simply because /ti/ is very rare and occurs only in recent borrowings so it makes more sense.
Of course <王> and <追う> sound quite different, but are both entered with <ou> and selecting the appropriate characters from the dropdown.
It really is neither phonetic nor phonemic.