You don't get motion sick on a treadmill because you're not wearing a VR headset. There's no forward motion of your head captured with your eyes to mismatch what your vestibular system is feeling.
To add to your point, there is a somewhat unpleasant sensation once you get off the treadmill, i.e., even if you are standing in place, it feels like you are moving forward.
This is incorrect. You don’t get motion sick on a treadmill because the small accelerations and decelerations match what your eyes are seeing. There is motion.