You didn't mention nitrAtes. Those are the end product of the cycle and build up. Water changes help to remove them. As long as your tank is cycled you SHOULDN'T have ammonia or nitrites anyway; but you WILL have nitrAtes.
Regardless, even if you have NO nitrates (which is pretty darn near impossible - unless you've got an incredibly heavily planted tank), you still need to perform regular water changes. Ammonia/nitrites/nitrates, etc are not the only things present in the water. There are other elements that we do not test for. There are innumerable numbers of other organic wastes that are present that get "reset" with each water change. Heavy metals are one example of things that need to be removed through water changes.
Also, fish absorb many of their minerals/vitamins through the water column. Failure to replenish that stock of minerals means that they do not get replaced, and therefore the fish cannot absorb them.
Water changes need to be done to remove the nitrates and excess minerals/heavy metals and to remove other organic wastes.