Example: in PR python/cpython#110848 Antoine is surprised that the PyThread_start_new_thread() function is part of the limited C API but is not documented.

We should explain that in the past, we didn't pay much attention to document and tests all limited C API functions, and that some functions were added to the limited C API by mistake. The limited c API was even "the default", before there was a clear cut between limited and non-limited, by creating Include/cpython/ sub-directory.

While the API can be inconsistent, it cannot be changed all sudden. We are not going to remove undocumented functions just because they are undocumented. Documentation can be written. Functions can be removed, but following PEP 387 deprecation process.

The only exception that I saw is when a function is part of the limited C API but cannot be used in the limited C API since it's broken: in that case, it can be removed immediately. I did that for the "trash can" API which was always broken. Same for PyWeakref_GET_OBJECT(): the implementation uses a member of structure whereas the structure is not part of the limited C API.