The busybox image is a good starting point. Take that, then copy your executables and libraries. If you are willing to go further, you can rather easily compile your own busybox with most utilities stripped out. It's not time intensive because you need to do it just once, and it takes just an afternoon to figure out how.
"The tooling makes it too easy to do it wrong." Compared to shell scripts with package manager invocations? Nobody configures a system with just packages: there are always scripts to call, chroots to create, users and groups to create, passwords to set, firewall policies to update, etc.
There are a bunch of ways to create LXC containers: shell scripts, Docker, ansible. Shell scripts preceded Docker: you can write a function to stop, create an intermediate tarball, and then proceed (so that you don't have to run e.g. debootstrap without a mirror every time you manually test your system build script; so that you can cache build steps that completed successfully).
With Docker images, the correct thing to do is to extend FROM the image you want to use, build the whole thing yourself, and then tag and store your image in a container repository. Neither should you rely upon months-old liveCD images.
"You should just build containers on busybox." So, no package management? A whole ensemble of custom builds to manually maintain (with no AppArmor or SELinux labels)? Maintainers may prefer for distros to field bug reports for their own common build configurations and known-good package sets. Please don't run as root in a container ("because it's only a container that'll get restarted someday"). Busybox is not a sufficient OS distribution.
It's not the tools, it's how people are choosing to use them. They can, could, and should try and use idempotent package management tasks within their container build scripts; but they don't and that's not Bash/Ash/POSIX's fault either.
This should rebuild all. There should be an e.g. `apt-get upgrade -y && rm -rf /var/lib/apt/lists` in there somewhere (because base images are usually not totally current (and neither are install ISOs)).
`docker build --no-cache --pull`
You should check that each Dockerfile extends FROM `tag:latest` or the latest version of the tag that you support. Its' not magical, you do have to work it.
Also, IMHO, Docker SHOULD NOT create another Linux distribution.
When bootstrapping a VM or container image it's the same principle (imo), it's safer to once think about what is needed and have that locked down and under control rather than having to keep track of what else was forgotten or might be suddenly a flaw in this ever changing "threat landscape". E.g. the libpng example from above: What else is lying around that is suddenly vulnerable tomorrow?
If you got time to compile your own kernel then why not. It's a process IMO and I usually get to that stage once everything else is locked down. To start a minimal set-up using alpine (or busybox) instead of ubuntu or whatever is already a huge reduction of attack surface (and complexity). Next I want restriction of all system calls on a process basis (if a syscall isn't whitelisted for this specific process it's an error). Once this is in place I might think about the kernel but in my scenarios this is rare. It really depends what your service does (what you want to protect).
It's imo less work (less maintenance costs) in the long run and always knowing what you have (and why) rather than having to think "oh I didn't know there was foo too? what does foo do"? Because as code changes and as you ship updates you will anyway be attending to updates that suddenly break your setup (and run against your whitelist). But doing this review/audit during an upgrade with a system that suffers from "feature and scope creep" is impossible (at least imho).
generally the less I have installed the less I need to track what might be suddenly a problem. Once my container/VM image is the way I want it I push it to my own docker registry and only deploy from there to production.
EDIT: really good talk on docker security (not just microservices) https://www.youtube.com/watch?v=346WmxQ5xtk