I agree this is possible, but the tools are somewhat obscure and slow. You can debootstrap in a chroot and then install packages, but it takes a long time, and likely re-downloads hundreds of megabytes packages you already have on the system.
I don't like Docker, but I think it does some differential compression with the layers when you are modifying the image. So you don't have to re-do this install from scratch.
You may also run into issues with user IDs and various system config files in the chroot. Configuring the service with flags, env vars, and config files is a bit of a pain.
Docker is essentially a glorified chroot... I've essentially tried to rebuild it, and it is unfortunately a lot of work.
