I see this as the main tension in the extracting-class viewpoint. Assuming your language allows it, you can extract out a class that's still private to the current package, meaning that the public API is unchanged. But there are still costs to extracting out that class.

If the one public method just calls private method A, B, and C in order, passing the result of one step to the next, and if we don't need to handle different variants of A, B, and C (meaning dependency injection is not necessary), we arguably don't gain much from splitting the original class in two. We're left with a very small class of a single method that's tightly coupled to the extracted class. We can remove the coupling with dependency injection, but now we need to add some code that actually injects that dependency at runtime. So understanding how the pieces fit together is harder. The only benefit to splitting the class that I can think of is in preparing for a future situation where orchestrating the three helper methods becomes more complex, or where you actually do need to handle different variants of A, B, and C via dependency injection. But it feels like premature abstraction to me, single responsibility principle notwithstanding.