In that thought experiment, wouldn't it even be more devastating the massive extinction of not only all human life but most life in the planet (or possibly universe, like in "the last question" from Asimov) when that "magic" of immortality leads us to our own self-destruction in an exponentially increasing immortal over-population that keeps consuming ever decreasing resources? That, or we'd have to be forbidden from birthing new life, so we'd be replacing death with the denial of life for future generations. Is that ethical?

Either way, that "magic" would be a problem, because it would make it much easier for a group of humans to mess things up. You can't just impose control over death and birth like that, not everyone is gonna agree with you, neither "sterilization" nor "euthanization" would really be a "solution" if people are not accepting it willingly. A system seeking control over life and death in a calculated and artificial way governed by humans is likely to fail horribly.

I believe that the needs of humanity as a species outweigh the needs of any particular individual human, or even any one particular generation of humans from a specific point in time.

Our evolution is proof that the death/birth cycle is extremely beneficial for our development as a species. If life were immortal it's likely we wouldn't have ever gotten past the primordial pond.

A life being replaced with the next allows for a sustainable stream of life... yes, I will ultimately die, but in doing so I'll be making space for someone else to be born, more human lives would exist, more opportunities of experiencing and enjoying life, new eyes to explore and learn from new points of view. In my mind those things are the whole point of us existing as a species. If you are stuck with a fixed set of immortal people then you are essentially denying a lot of new humans from their opportunity to exist. I don't think that would be good for humanity.

We cannot all exist at the same time... if we figured out a way to do that then things might be different, but that's not the same question as the one being discussed here. We can't just hand-wave the problems caused by immortality and assume that they will be fixed somehow sometime, cos with that logic one could justify almost anything.