If your tires are worn down, you might not notice right away. You would expect to feel a gradual increase in stopping time, a gradual loss of traction that allows you to gauge by feel when to replace your tires.
Unfortunately, thanks to a quirk of physics, that's not the case.
See, your tread isn't what gives your tires grip. The grip of your tires comes from the contact of rubber on the ground. Balding tires with thin tread actually give you more rubber contact with the ground, increasing your traction so long as it's dry.