Mourning is a natural part of life as much as death is. It isn't a waste if it is done in moderation. You treat it as if life should purely be about efficiency, which is mechanical and artificial feeling. Life should be organic in that we experience death and realize that while life is fleeting, it should not be taken for granted. If it's about your personal feelings on death, then make your funeral different, like the Louisiana ones where there's a freaking parade almost. But you can't use mourning as a basic human practice related to death as an argument for why immortality is superior, since that reduces humanity to just living and no sense of change, no loss, no give and take.
It shouldn't be about a competition, it should be about seeking knowledge to benefit others and oneself.
If it is an individual immortal, the likelihood of being a hermit increases. But even a group of immortal individuals are not by necessity going to remain social beings forever. Even if there isn't any physical degeneration, we have to consider the psychological aspects of such a prolonged amount of social interaction with no sense of the significance of life in its transience. If I just experience something in perfection forever, I cease to truly appreciate it.
This is a matter of time, though, which still could be comparatively measured, if not on a much larger scale. Eventually the possibilities would dwindle down, even if it took ten thousand or so years.
Unnatural and artificial are markedly different, however. Unnatural is something going against the natural order of things, such as someone trying to create a disembodied existence. Immortality is similar in that it is almost a necessity that things die. The population control consideration has to be brought up too. We have a cap as to how many people can live on this planet and even if food and drink weren't options, there is always the possibility of peoples' baser natures coming into play.
If you have no seeming limitations at all, such as no need for food or water, even sleep perhaps, then immortality would become the worse kind of existence, since you would have no sense of time's limitations, since there would be nothing holding you back. And even if there was, we project a huge amount of time that overrides any of the hindrances of food/water/sleep, so eventually there would be a sense of apathy, in that you have no real motivation, since you can put something off indefinitely.
Assuming there is a remote cutoff point, then immortality is merely delaying the inevitable, since immortality is not necessarily the same as indestructibility. If heaven or some such afterlife is a factor, then that becomes a living hell, does it not? It's one thing to propose a secular immortality, which by its nature would have a limitation of billions of years assuming this solar system outlives its usefulness. And even the universe itself cannot continue forever, so there is a cut off point regardless. But my critique is especially directed towards supernatural immortality, where there is no time frame