The phonic connection to reading is overrated IMHO and this is why I wrote of a hack of the visual system. Kanji/Hanzi are so easy to read because over the millennia the ones that are hard to recognize at speed have bene dropped or tuned -- and they have no connection to sound, as you say (well, in the Japanese case in particular there are some phonological puns, but I doubt you notice them at speed, even if you have the historical connection). In the latin alphabet I almost never recognize puns when reading (though I get them immediately if someone is reading aloud). And when I was learning German I struggled at first to read the compound words but now the morphological decomposition is automatic.
In fact I think the trend to teach kids English via "phonics" makes spelling harder; comment back if you want to discuss further