How nice that nature has chosen the correct solution for your host of terrifying problems. If we were immortal and truly wise, I'm sure we also would have decided it was reasonable to kill literally everyone in order to share resources better.
And if you don't think natural selection is what powers nature, then the question becomes, why did God choose to kill his creatures?
So it would likely be pretty unchanged from our current levels. Just about everyone survives to produce children these days (with some people i wonder how).
Also i don't think when people say conquer death they mean true immortality, they mean Negligible senescence i.e. we are no more likely to die due to aging, people would still die (accidents, violence, natural disaster etc).