Doesn't solve the issue of needing a C compiler for third party extensions, and definitely qualifies as a work-around for the existing toolset.

Yes, it helps. But you can use Docker with Go programs as well (and drop a lot more of the base image in the process).

The way we do this is to have a base image that has already yum installed or pip installed all modules (non trivial, anyway) that our package needs. Then the docker image that needs to be rebuilt (that depends on the first one) is just a minimal pip install away.

Actually, nice thing about docker is you can build a compilation container (pre-built with all your C/C++ apps ready to go and shared amongst your coworkers), compile your extensions using that, and then only install them into your target container (sans compilation tools). It's a little more grunt work that way, but you get better control and reproducibility without the explosion in image sizes.