This is called a straight skeleton, and there is no such operation in inkscape or any other graphics design application for that matter. But you can make a straight skeleton by insetting the surface copy several times and then finding where the edges meet. This is how the algorithm works too.
Now if you manually follow the algorithm and inset enough you will find the points of intersection and where the centers amass. Doing the algorithm manually results in:
Here is a paper on how you would do it. As you see its not a perfect method since it does not always yield clean results. Like in the K. If this glitch is not desired then there is no framework, that we know of, for making this fully automated. (note there would be a glitch on top corner of P too but i fixed it since it was less work to draw that way)
Now it is true that you could use fonts that are already single line. But then your limited to what others have already done for you. But then even if you would have a inset function you'd end up doing manual tweaks.