Yes, and it's not an academic exercise: it's being used in Guix (together with related projects such as stage0, M2-Planet, and Gash) to build everything from source starting from a 357-byte program:

https://guix.gnu.org/en/blog/2023/the-full-source-bootstrap-...

This gives the level of auditability and transparency that we desperately need.

However, the same problem of "yogurt software" manifests at higher levels of the stack, typically with compilers and build systems, some of which still cannot be built from source (GHC and Bazel come to mind).