How can I change the screenshot defaults to save the image to desktop immediately?

Press command-shift-5, then click Options and disable "Show Floating Thumbnail".

tharper wrote:

I knew of this, but thanks.

My goal is to save the screenshot instantly with no further action required.

And that's how you do it! Change this once, use always.

After you make the change I described, just use Command-Shift-3 or Command-Shift-4 and it will work as it did before Mojave, saving immediately.