Behind such a strange title are the motivations for the server that you will optimize needing to be headless. Even though BeagleBone is able to display GUIs, shiny graphics, and desktops, you need to get used to interacting with your server as if you are in a cave with limited light and no eye-candy gadgets. Here are some of the reasons why:
Resources: The most important reason is that a graphical desktop consumes the most amount of resources. Consider not only the GUI resources but also the graphical server it relies on; therefore, it needs more CPU, memory, and disk space.
Space: Our server can be physically anywhere. Thanks to its reduced dimensions, it is easy to put BeagleBone in a place and forget about it. This can be next to the desktop, behind your monitor, in a cupboard, and in your car as well.
Access and simplicity: If you need to get access to a server or maybe several servers, you will really not want to bother connecting to each dedicated server. If you need to administer 11 desktops, this will require you to connect to each one. On the other hand, by using a console environment, you are ensured having the same behaviors each time.
Among others, these reasons justify the time that you are going to spend on your experiments. It's worth it.