I was referring to direction, deceleration and acceleration on the classic digital joystick.
Indeed. It may be more accurate to sample quicker, but if someone presses left then right, then lets go of the joystick entirely, all within a screen redraw - your game does not need to know that. In fact if your game DID react to that action it would seem like the game is not responding correctly to user input, as far as the person at the controls was concerned.
This cannot be compared to audio where you are trying to replicate an analog signal by digital means, so naturally the more detail you can record the better. Whereas you do not need to record exactly what the persons hands are doing to sufficiently replicate what the game needs to know to react fast enough for it to appear seamless to a human being.
Maybe if we 1kHz refresh rates on our TV/monitors we could perceive the difference (even if we cannot outright see every single frame itself) but we do not. Its just logical that if you have a 60Hz screen update then that is the absolute fastest you need to update your game state and so the fastest you need to capture joystick input.
All your game needs to know is the state of the joystick right at the moment it needs to take action based on that input. You are only going to take action once per screen redraw or again, it will appear to the user that the game is reacting oddly to user input.
In fact, most games may react even slower. I remember distinctly that some games seem too sensitive to user input and could have done with making sure you are pressing the same button for several screen redraws before reacting. Its all about synchronising the game response with the users reaction time.
So again, the polling speed of the Amiga joyport is no more useful for gaming than USB1. Alas a PC keyboard seems pretty slow to react but its still "fast enough" for most games, to the point that home-made MAME cabinets using PCs just have a little keyboard emulator circuit wired up to the joystick and buttons.