The counterpoint here is that shipping the compiled binaries reduces a ton of uncertainty in terms of package version or compilation with non-standard options (cue potential reproducibility problems). Also different OSes will put libraries in different places (including different Linuxes). The last major benefit is that most OSes require root permissions to install packages, so Julia's approach works a lot better on systems where the user isn't root (e.g. most servers), and also means that the package manager doesn't have to know how to talk to the OS package manager for every OS that we support.
Lastly, if you want use system versions of C/C++ packages, you can do so using the preference system (see https://docs.binarybuilder.org/stable/jll/#Non-dev'ed-JLL-pa.... This isn't the default because it would make package installation a lot more annoying, but for deployment it very well may be what you want to do.