Asking a functional programmer to always write continuations by hand is the same as asking an object-oriented programmer to always set up and use virtual method tables manually.
Remark: The continuation passing style is a fine internal representation for the computer. It may also be suitable for human use in some, but not all, applications; although all such applications I have seen are better expressed in monads. (Transforming non-tail to tail calls is not one such application; it should be automatic.)