I was recently on the Microsoft Developer Network website (aka MSDN) looking at some API documentation. Many of the more popular APIs have code examples so the developer can see example usage rather than have to try to understand every nuance of the API before using it. The particular API that I was looking to use had an example, so I made the unfortunate decision to look at the code. The example was a turd. It wasn't a polished turd. It was just a normal, run-of-the-mill turd. The code had HANDLE leaks, memory leaks, and a bunch of other critical issues. It looked like it was written by a 20 line Norris Number programmer (aka newbie).
Being rather bothered by this, I set out to learn how Microsoft produces its code samples. According to one source I found, the company hands the task off to interns. So, sample code that a whole bunch of other programmers are going to simply copy-pasta into their own code is being written by amateur programmers. Nothing could possibly go wrong with that. If the examples are indeed written by interns, it certainly explains why the quality of the code samples in the documentation is all over the map ranging from really bad to barely passable. It's certainly not what I would expect from a professional organization with 50,000 employees. If you open a HANDLE, close it. Allocate memory? Free it. Simple things that aren't hard to do but help achieve a level of professionalism because you know that other people are just going to copy the example into their code, expect it to work, and not have unforeseen bugs in production.
MSDN is the face of Microsoft most people don't really get to see unless they start developing for the Windows OS. But it matters who produces the documentation because a single mistake is going to affect (tens/hundreds of) thousands of applications and millions (billions?) of people. API documentation is almost always too intricate for most other developers to fully understand. While it is the be-all-end-all definitive overview of any give API call, code examples provide context and meaning. A lot of people struggle with "so if I use this API, what do I do next" but have the "aha!" moment when they see a working example connecting the API to other code. Developers will copy and paste an example long before they fully comprehend any given API. For this reason, code examples need to have the same care and professionalism applied to them as the API itself. Passing this responsibility off to an intern is going to create significant long-term problems.
Writing your own code examples for an API also has the benefit of revealing bugs in the API. If the developer who made the API is writing the documentation for it and the code sample, they are 15 zillion times more likely to spot mistakes and correct them before they get released into the wild. Pass that responsibility off to an intern? Well, the intern is going to not run into or just ignore the bugs in the API because THEY DON'T CARE. They want the paycheck and the checkmark on their graduation forms that says they did their internship. Users (developers) have to live with the disaster that interns leave behind in their wake. Putting them on documentation and code example writing tasks means interns will be the face of the company that developers (i.e. the people who matter the most) will see. That strikes me as unprofessional.
In short: Develop an API? Do your own documentation and code sample writing. Is it tedious and boring? Yes. But it is important to do it anyway. In fact, it is infinitely more important than the API you wrote.