It's not some technical impossibility - I think it would make sense to make this possible, at least in GUI Emacs. I suppose there was never a strong incentive to tackle this problem.
This is indeed not possible in a classical terminal emulator (don’t know if kkp for example has extensions for it). But most GUI apps can detect individual modifiers being pressed and released, even as separate events. Some editors like VSCode can also bind modifier taps to actions using this ability. In Emacs however this is AFAIK not possible even in the GUI, because of how keybindings are handled deep down.
The UI pattern described by the GP does exist in some other apps and platforms. For example, if you connect an external keyboard to an iPad, holding down the Cmd modifier for a couple of seconds will show you a popup which-key-like overview of all Cmd+key keybindings.