You need to learn Latin, Greek, French, and German at a minimum if you want to be able to reliably deduce spelling from sounds once you're past the elementary level.
Reliable spelling is pretty irrelevant, especially in the age of spellcheck. Phonics is about READING. Understanding Latin, Greek, French, and German will certainly help with advanced etymology, but you don't really have to know the history of the bi- prefix to understand it means "2." Learning multiple languages is always a great advantage. . .but you want to teach reading in all those languages with phonics.
Whatever criticisms you have of phonics, I challenge you to cite an alternative method of teaching reading that is equivalent, let alone better. Empirically, no other method has been able to effectively teach reading.