The comment above is more of an explanation of how this currently works in Blender and how one can approach the aforementioned challenge.
I do agree that the Python API is often just a thin wrapper around the C/C++ code [0] and that the documentation of the required context for operators is a bit lacking for people who are not familiar with Blender's implementation. This is also acknowledged in the API docs [1]. However, I do think the API is quite usable and not particularly complicated to understand.
[0] https://docs.blender.org/api/current/info_gotcha.html
[1] https://docs.blender.org/api/current/info_gotcha.html#why-do...
When you have issues with calling an operator due to a wrong context, there are different ways to approach the problem:
1. Figure out what the necessary context is and switch modes, areas, etc. to match the requirements.
2. Figure out what the necessary context is and override the context.
3. Avoid using operators.
Approach 1.) could be accomplished by checking where the operator is originally used in Blender. For instance the `bpy.ops.mesh.remove_doubles()` is available in edit mode in the Mesh > Clean up menu. Thus edit mode is required to run the operator. This will work for many operators because they don't have very complicated requirements.
Approach 2.) is for when you must use an operator, it requires a complicated context and you know about Blender's internals. You can look at the operator's (poll) implementation and construct a specific context that is passed into the operator [0]. This should only be used if there is no better alternative.
Approach 3.) is preferable when you are working with mesh data. Instead of using regular operators you can use bmesh instead [1]. It doesn't require switching to edit mode or passing a context. It's usually the more efficient approach as well.
[0] https://docs.blender.org/api/current/bpy.ops.html#overriding...
[1] https://docs.blender.org/api/current/bmesh.html