Why a community might want a Python Software Foundation
I'll start by noting that the bulk of my involvement with these entities has been indirect at best. I am a member of the Python community, but haven't had many direct involvements with these organizations. That said, I've seen the benefits of their hard work.
To start, it's useful to know what it is these entities actually hope to accomplish.
The PSF's stated goal is to "promote, protect, and advance the Python programming language, and to support and facilitate the growth of a diverse and international community of Python programmers."