Why do some radicals not get taught until several levels after the same Kanji (eg Music or Fault)? Why wouldn’t WK teach us the Radical first and then the Kanji?
Only the overlords can answer you 
Radicals are used as mnemonic components. Thus kanji can be reintroduced later as radicals so that they can be used to simplify the mnemonics of more complicated kanji.
For example, 屋 is taught as a kanji at level 9, introduced as flag + ground + private + dirt. It’s then reintroduced as the radical “shop” in level 42, allowing 握 (on the same level) to be taught as fingers + shop, rather than fingers + flag + ground + private + dirt.