If I start the game without a gamepad attached to the computer, and then attach the gamepad, I'd like to use the gamepad without restarting the game. And one would expect that polling the attached input devices should never take hundreds or thousands of milliseconds, there must be something seriously wrong in the Linux input device stack or maybe in one of the input device drivers.
Or maybe just poll for new input devices when the game is paused, or before the game starts.
Then you still have problems to handle like accidentally disconnecting/reconnecting the gamepad when somebody stumbles over the cable (for instance the game might want to automatically pause if the gamepad suddenly 'disappears' for any reason). Gamepads should be automatically detected at any time in the game as they are connected or disconnected. That's how it works on game consoles, and PC games shouldn't behave any different in that regard IMHO.
The input stack is fine, this game disabled the things that would let it work nicely (see upthread discussion of SDL supporting udev and inotify)