The productivity gains don't come from increased typing speed. They come from the ability to script and automate most, if not all, of the administration and setup tasks from the command line.
The first time a system is built will always take a significant amount of time. It's the ability to quickly and easily replicate the process that saves in the long run.
For example frameworks save on setup by providing a scaffold to build on. Package management systems (ex apt-get, npm, etc) save on the time required to build, update, manage dependencies. Provisioning (ex puppet, chef) save on setup and administration of full system builds. Containerization can be used to standardize development and production deployments.
If the processes can be scripted, versioned, and shared publicly via open source platforms and package registries then the initial setup can be reduced to nothing more than finding and gluing the right pieces together.
Windows is still years behind the curve on automation simply because the ecosystem still builds on the assumption that everything should be configurable via a GUI.
It's not so much, keyboard vs mouse as computer vs human. Automation will always produce the greatest gains in productivity and automation is best left to the command line.
