How to save still renders straight to disk like animations? Animation frames get saved to disk automatically. 

Still images do not. 

Is there a setting that can be changed so that single-frame renders also get saved to disk automatically upon completion?

To clarify, I mean changing the behavior of the render function, not simply changing the frame range to Start:1 End:1 (for example) and rendering as an animation.
Yes, this is supported.

"Write Image" - it's an optional parameter of the operator, and can be set in the key-map editor.

(Preferences > Input > search "render")

In my case I have the shortcut for Render set to CmdR so it looks like this:



Just make sure to specify a file name: