The jgraph Java toolkit and mxgraph JavaScript library used in draw.io both support automatic layout even for quite large networks. From the draw.io gui I've never used it but I would be surprised if the possibility does not exist.
draw.io has some automatic layouts (Arrange > Layout), but they are fairly basic. In terms of customizability it doesn't come close to yFiles / yEd. (Admittedly, I'm biased; I work for the latter, but the available layout options do indeed speak for themselves.)
yEd is freeware. You can see the license by clicking one of the download links. I guess they monetize it by licensing the underlying diagramming libraries to businesses from the looks of it.
The underlying graph drawing library for WPF, yes. yEd itself is built on the same layouts, but a different rendering platform with Java Swing, of course.
I waste zero time re-organizing as I create charts, so I don't lose thoughts while trying to make sure the boxes are organized.
TIPS:
* F2 - change the caption on your shape
* F6 - update properties of the shape/connector
* Layouts - experiment with clustering to get cool insights!