I was thinking about this sentiment:

  And that "one single place" is for this trivial toy program. Now imagine the impedance across the delivery of a real business app.

That seemed very incongruous with my experience. I think the problem is that in my experience the number of types necessary scales sub-linearly with the amount of code. This is because Haskell (and other languages with what one might consider pleasant type systems) generally have full type inference. So while you might need the explicit type for the toy example, scaling that example up means only a handful, and possibly a net negative, other necessary explicit types.

This comes up in a concrete manner in your example. The add function is almost too small to be typed appropriately. There isn't enough information for GHC to constrain the choice of numeric representation so it picks one. If you were to embed that in a larger program with more specific operators no types are necessary.

  Prelude> let add = (+) <$> readLn <*> readLn
  Prelude> let foo = (/) <$> add <*> add
  Prelude> foo
  3
  30.1
  40
  10.2
  0.6593625498007968

So it's quite possible that the "type burden" becomes smaller as your system grows.