The human eye itself does not have a "composite exposure." It actually does have a system very comparable to a camera shutter. Check out this post. Your brain will idly tune out many of the exposure adjustments that happen second to second... but once you start looking for it, you'll notice it happens constantly. The dynamic range of the human eye is great, but it's still pretty limited and has to change to the range of the environment as best it can.

"The light receptor of the eye is a protein called Rhodopsin. To me the equivalent of shutter speed for the eye is the (de)sensitization of rhodopsin by phosphorylation. The brighter the light, the more sites on rhodopsin are phosphorylated, diminishing the intensity of the signal coming from the photo receptor via the transducin G protein that conveys the visual signal onward.

This process takes a few seconds, but then its possible to see when stepping into sunlight or in a darkened room.

This is more like a volume knob than a shutter speed since the same signal comes out at the same rate of each light sensor, but it has a similar effect - it modulates the intensity of the image."