I would not remove them, but place them elsewhere, linked from the point you should run them at the install process.
It's very useful to have a complete 'getting started' page that get you from zero to working, without assuming that the reader understands what every intermediate step means. But as you said, the parts that are dependencies for other products can be encapsulated so that savvy users can skip them easily.
The instructions to install Docker are clearly wrong on many Linux distributions. They add very little value, and are yet another thing that has to be maintained.
The docker installation script is for Ubuntu. I added it to help some users get started pretty quickly.
On the installation page, there is a link to the official Docker guide which comes first. That should help other users with an OS-specific installation guide.
It's very useful to have a complete 'getting started' page that get you from zero to working, without assuming that the reader understands what every intermediate step means. But as you said, the parts that are dependencies for other products can be encapsulated so that savvy users can skip them easily.