The process in the OP—starting a VM in Virtualbox, and having Docker use the VM—is basically a manual version of what docker-machine does automatically.

https://github.com/docker/machine

Even though it's all a VM under the hood, docker-machine makes it all feel a bit more streamlined/native. Also, the version of Linux it uses—Boot2Docker—will likely start up more quickly, and probably use slightly fewer resources as well.

I'm using docker-machine so I can run Docker on OS X 10.9, which predates Docker Desktop (and Hyperkit).