I'll have to watch the video below, but don't you have to write some sort of Rust wrapper for every definition in Python.h? What about macros like Py_INCREF and Py_DECREF? I'd guess that someone has or will eventually do that work, but it's yet another layer of complexity, which can have the same downsides as SWIG.
For better or worse, the Python C API is tighlty coupled to the C implementation. That makes it very difficult to be more natural and understandable than C. It's a fairly huge API: https://docs.python.org/2/c-api/index.html
People always try to cover it up with "nice" abstractions, but they invariably end up being leaky (e.g. with respect to threads, garbage collection, OS portability, etc.)
Another huge can of worms: the build system. With a plain C extension, all I need is a C compiler on the system, and I can just do "python setup.py build". The situation with Windows is also quite messy -- I can't imagine Rust making it better.
I have experimented with creating normal .o files from OCaml and linking them with .o files from C/C++. That is a great feature of the OCaml toolchain. Still, I remember the documentation being sparse and I don't even remember how I did it at the moment.
FWIW, my main language is Python, but I love OCaml for certain things, and have grown to like C++ as well. Rust seems very interesting to me for its security properties and because it has native threads rather than including a mini-OS in the runtime like Go. My understanding is that Go is hopeless for many kinds of Python extensions, precisely because of the runtime issue, and calling from Go back into Python. (at least this was true a year or 2 ago)
I'm always wary of creating more layers than necessary. A system composed of Python and C will necessarily have fewer layers than one composed of Python and Rust, simply because Python is written in C and its interface is defined in C.
EDIT: I left out the BIGGEST point -- a dealbreaker. Python does NOT have an ABI. It has an API. AFAIK, that means you have to write a Rust ABI-compatible wrapper for EVERY VERSION of Python.
https://www.python.org/dev/peps/pep-0384/
To make a generalization, programmers learn about C APIs before they understand what the ABI is. It's just more concepts that you need to know about to write correct code. So if you just want to speed up an existing Python program, I would still recommend using a simple C or C++ extension. This solves both single-threaded speed issues and give you parallelism with multiple cores, so you will get huge speedups.