We use Alpine Linux for our applications and I like it, and I too shudder at it being used for the entire production system. As a sysadmin, you can still administer the LTS distro that hosts the docker containers and whatever other pieces of the stack you interact with. Alpine Linux containers, like any other container, should host an instance of an application (maybe not even that, depending on how complex the application is) -- not the entire production server, not SSH keys, not iptables, firewall rules, etc.