I can watch a 30 FPS game, and possibly use a game controller and everything is fine. It's not spectacular, but it's not bad. With a joystick, you do not notice the latency, and they control the speed at which you turn, which disguises the problems of low FPS.
Once you move to a PC and use a mouse to aim and change the view you see in 1st person or over the shoulder, things change. With a mouse in hand, you gain a far more precise input device. When you move your hand fast or slow, the view changes with it. With this type of input device, 30 FPS causes latency which you can notice.
I personally notice this latency enough to get nauseated within a few minutes, and if I attempt to play through it, it leads to headaches within 30+ minutes. Gaming is not worth a headache or nausea.
At 60 FPS I can tolerate a lot more. It takes 30-60 minutes for me to become nauseated, so I can play, but take frequent breaks. It takes 80+ FPS before I no longer get nausea issues directly related to the input device. I still can get nausea if the game has a bouncy running animation, but normal smooth game play no longer makes me sick.