Save board selection with sketch?

adwsystems:
I don't know what is in the *.ino file.

It's just a text file that contains your sketch code. There's no hidden magic.

adwsystems:
But I can't see that it is that big of a change.

Then please submit a pull request. You would probably want to follow the approved convention established by Board autoswitch by timkoers · Pull Request #7349 · arduino/Arduino · GitHub but with the missing requirement of command line tool support (rather than being baked into the Arduino IDE code):
Autoselection of device · Issue #1481 · arduino/Arduino · GitHub
I think it will have a very good chance of being accepted.

As the saying goes: "Be the change you wish to see in the world".

adwsystems:
Can the *.ino file be used for any other purpose than for the Arduino IDE? (ie., is there another application or compiler that can use it)

Sure. There are all sorts of alternatives to the Arduino IDE: PlatformIO, CodeBender, Atmel Studio with the Visual Micro plugin, Eclipse with the Sloeber plugin, Visuino, Ardublock, Andruino, etc.