This does not make sense to me . Selecting, for example, "Wingdings 2" causes keystrokes to be displayed as I expect. There is no a priori reason that "Apple Symbols" can't behave the same way. The screen appearance of a keystroke is not a property of the Unicode, but of the application's metadata.
The way it is supposed to work is like this: The keyboard produces key codes, which are translated into Unicode values by the MacOS mapping files, which are then translated into glyphs on the screen by the active font. The app normally plays little role, and standard fonts all produce the same unicode characters. Symbols and characters from the scripts used by other languages are produced by changing the keyboard layout instead of the font, or by using a utility like Character Viewer.
But there are some legacy fonts held over from the past which are non-Unicode and a some apps will recognize them, so that sometimes you can use the keyboard to type symbols instead of normal Latin letters. But text produced this way will most likely revert to Latin when copy/pasted to another app or transmitted to another system, so it’s best to avoid this if you need to ensure what you produce is always seen as you intended.
If MS Office does what you require, by all means use it. But I don’t see Apple ever going back to non-Unicode systems and having the characters created by keystrokes determined by the font you choose. Instead any non-unicode left overs that still do that will eventually disappear.