There have been several ports of Python to JS or to wasm over the years. Pyodide is the most mature today, but another interesting one is pypy.js which ported PyPy and even included a JIT!
But I agree that CheerpX allows running more things. There will always be a use case for "just run an x86 binary" when you don't have the source code. But for things where the source is available a proper port to wasm like Pyodide will be faster.
As pointed out by another user, I was actually referring to compiling Python _directly_ to Wasm. Porting the C++ _implementation_ to Wasm is obviously possible.
Well, Pyodide does port CPython directly to wasm. You're basically running CPython on wasm instead of on x86 - it's just another architecture. That's the natural thing to do I think.
But I see what you're saying, one could also theoretically write a new implementation of the Python language that uses wasm in a more "direct" way. We are exploring exactly that right now using wasm GC, compiling Java and Dart objects directly to wasm GC objects and so forth. That approach still has a lot left to prove, and it may not make sense for all languages, and specifically, I'm not sure if Python would benefit from it at all. So that is very much unclear.
In practice, when you want to run Python on wasm today, I think Pyodide's approach of porting CPython to wasm is the natural way, and it works well. That's what I was getting at.
To be fair that's not just theoretical, the Pyodide project does exactly that:
https://pyodide.org/en/stable/
There have been several ports of Python to JS or to wasm over the years. Pyodide is the most mature today, but another interesting one is pypy.js which ported PyPy and even included a JIT!
But I agree that CheerpX allows running more things. There will always be a use case for "just run an x86 binary" when you don't have the source code. But for things where the source is available a proper port to wasm like Pyodide will be faster.