Sure, I think we can just ignore the fact that the Red Hat Core package manager was driven by Python for almost 20 plus years and only recently, as of two years ago, switched to C++.
You are correct at seeing C as a backbone, but most tools, especially early tools were written in a language like Python. Its easy to prototype and adopt.
I guarantee you if I go through a list of system tools that every Linux distro is dependent on, including something like a package manager, which the linux os is absolutely dependent on You would be genuinely surprised by the amount of tools written in a language like Python or Ruby.
Also, a package manager is not core to a Linux distribution, Really? That seems like stretch.
Yes, you can compile everything from source. Very few people do.