Every binary in the chain can be signed and reproducible (theoretically; we aren't quite there, realistically speaking, and the bootstrap, as you note, is tricky). Forcing every user to build everything from source every time is just a mess, and provides little benefit over signed (reproducible) binaries for the vast majority of users.
It sounds like you (and the guix project) are conflating two orthogonal concepts and making "reproducible builds" into a concept that won't work in widespread use, and maybe even has negative value. We want reproducible builds so that we can be certain that the binary a vendor ships us is built exactly the way they say it was. We don't want it so that everyone is forced to build everything from scratch every time.
Reproducible builds means we can build an identical binary from source to prove that it is what we think it is. It should not mean we must build an identical binary from source every time we install a thing.