How would you do it in many of those cases? For instance:

  ax[i] = bx[i]
  ay[i] = by[i]
  az[i] = bz[i]

Can the languages used write this in a better way?

I do agree that having inner functions and making them easy to define is better, but it's not always possible. In F# I could write:

  let assign i (a,b) = a[i] <- b[i]
  [ax,bx; ay,by; az,bz] |> Seq.iter (assign i)

But that's allocating a list (and if I closed over i, it'd allocate a closure too). Really good macro support would fix this, though. And it's only marginally better in this case. (For more elaborate cases it might be easier to scan.)