With each passage, ices are preferentially lost and dust is preferentially left behind. Thus, a comet will develop a surface layer that becomes enriched in dust, i.e., it becomes darker and a better insulator. Eventually, such a comet may turn so black and develop such a good insulating surface that it will turn off, continuing in its orbit but no longer looking or behaving like a comet. Clearly, comets can't do this forever. And if we accept the Copernican Principle, that this time in the history of our solar system is not special, then new comets have been appearing and getting used up for the entire history of the solar system.
Comets are sources of water.
Alternatively, one could wonder whether the Earth's present abundance of water was deposited here by impacts with comets, early in Earth's history. The Earth's oceans contain 1018 kg of water. Comets collide with planets. We witnessed the collision of Comet Shoemaker-Levy IX with Jupiter in 1996.