That the Godot scene editor is made with Godot seems to be an excellent example of how eating one's own dog food can exercise and improve the basic technology.
It's fairly common practice in compilers (for good reason), i.e. the D compiler is now written in D and the Rust compiler is written in Rust etc. I think the first Haskell compiler was written in Miranda but that's before my time.
You get to test the product without waiting for feedback from the real world and you also end up with a test suite (in effect) for free.
You compile the next version of the compiler using the previous version. That does mean that the first version of the compiler cannot be written in the target language. Once you've got that working you can write a new compiler in the target language and compile it with the previous compiler.
Back in ye olden days the first assembler was written in machine code. The first C compiler was written in assembly, and the first D compiler in turn was written in C.