I would consider the lack of a shell a benefit in this scenario. You really don’t want the extra attack surface and tooling.

Considering you also manage the host, if you want to see what’s going on inside the container (which for such a simple image can be done once while building it the first time more likely), you can use unshare to spawn a bash process in the container namespaces (e.g., unshare -m -p […] -t PID bash, or something like this - I am going by memory).