When I did my test (on a Mac with no external displays), I did not receive the conflict icon.
I just tested this on a different Mac that is setup for dual display (an iMac in Target Display Mode). On that Mac, Command-F1 normally toggles Display Mirroring, and Command-F2 toggles Target Display Mode. Once I enabled "Use F1, F2, etc. keys as standard function keys," Command-F1 and Command-F2 no longer performed those functions (they switched to Command-fn-F1/Command-fn-F2). I was able to assign Command-F1 as a shortcut, again with no "!"
So the likely reason you're seeing "!" is that you've already assigned Command-F1 to a function in another app (I've managed to do that myself from time to time).