For this sort of task, there's a remarkable amount of dead weight that can be cleared out. For starters, because your binaries are so small, serving them over PXE or the like becomes a triviality in regards to bandwidth. Your system will start faster because it doesn't have to do things like initialize the various pseudo-filesystems Linux has, or initialize the virtual file system, or any number of other tasks. This now means you don't need that hot, failure prone hard disk at all, nor its buffers and journals and other context switches that occur because of it. Because you've gotten rid of the hard disk, you've gotten rid of its heat, meaning you can pack servers more densely.
Similarly, you can eliminate a considerable amount of the networking stack. You know what the messages it's going to send and receive look like, and any other messages are going to be dropped anyways, so why have the code to handle them loaded in memory at all?
Because of their minimalism, microkernels allow you to ask a lot more fundamental questions about your applications. This means you can build a system much more oriented around your needs, with minimal superfluous framework. This now means your apps are faster, because they have to fight less OS bureaucracy, more reliable because they're much more simple, and more secure, because the system as a whole is smaller, and thus easier to audit. Sometimes, asking yourself what you don't need is just as important, if not moreso, than what you do need.