It's not an API if the methods are private or declared inside the method. I just rewrote a portion of code the other day with the discussed pattern because it made the high level step very clear:

  DoAll() {
    DoA();
    DoB();

    DoA() { ... }
    DoB() { ... }
  }

One thing I like about the "straight code" version is that it is clear that things are executed sequentially, and only one time. With named functions it is possible that they could call each other too.