Hotkeys are a touchy item, and they only fully work in certain places, while in other places only a subset of them work.
For example, when the Settings window is open, only the keys ESC and the function keys (F1 through f12) are enabled. The exception is the Controls tab, on which all hotkeys are enabled. The issue is input. The Settings window is for configuration, and to take the Game tab as an example, if hotkeys were active here they could interfere with simply entering configuration information. However, ESC and the function keys don't have a direct input function, so they can be active on configuration pages. Since the Controls tab is specifically for controlling the tournament and not configuring it, and they won't interfere with input, all hotkeys are active.
Granted, most configuration tabs don't have direct input fields like the Game tab, but for the sake of consistency the hotkeys are [mostly] disabled on the various Settings tabs. I guess I could enable hotkeys on those tabs, but I'm afraid it would be more confusing when the hotkeys work on some tabs but not others.