"My only complaint, and no one at Apple seems to have an answer either. I got the Magic Keyboard w Numeric Keypad (top in pic below), and it has F13 thru F19 function keys. They don't have any purpose that I can find, and they're not programmable without a third party app - that seems very odd to me."
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I have programed my F keys 13-19 to do various things for me quickly.
The one I use very frequently is F19 which I changed to activate taking/saving a
screen shot of a selected area.I have my trackpad next to my keyboard so it's just a matter of moving my finger about an inch or 2 to activate.I don't know if this is the kind of thing you were talking about-that's Very simple. No need for an app.System preferences>Keyboard>shortcuts.