In almost all situations, brakes can exceed the traction the tires have to the road, so applying additional braking force to the wheels will not allow you to slow down more quickly. To put it another way, apply brakes "too hard" can already exceed the tires ability to slow the car down through friction with the road, as can be felt when the car slides while you're trying to brake. ABS is a system that keeps brakes from locking up by lessening the braking force applied to the tire to the point where it has traction again or is within it's braking threshold.

One thing that isn't touched on here is that engine compression applies a passive slow down and can be very important for situations where your brakes might overheat, such as descending a steep and long hill.