People aren't 'born' in the normal sense - instead they are 'fluctuated' into existence as full-grown adults. Instead of normal 'death', people simply dissolve painlessly after a given amount of time. Nobody is aware that at some point in the future they will 'die', and whenever someone does all currently existing people have their memories instantly modified to remove any trace of them.

This scenario is way, way worse than the real world we live in. It's bad enough that some of my friends and loved ones are dead. I don't want to lose my memories of them too. The social connections people form with others are one of the most important aspects of their lives. If you kill someone and destroy all their connections at the same time you've harmed them far more badly than if you just killed them.

Plus, there's also the practical fact that if you are unaware of when you will "dissolve" it will be impossible for you to plan your life to properly maximize your own utility. What if you had the choice between going to a good movie today, and a great movie next week, and were going to dissolve tomorrow? If you didn't know that you were going to dissolve you'd pick the great movie next week, and would die having had less fun than you otherwise could have had.

I'd prefer option 1 in this scenario, and in any other, because the title of the OP is a misnomer, people can't be replaced. The idea that you are "replacing" someone if you create a new person after they die implies that people are not valuable, they are merely containers for holding what is really valuable (happiness, utility, etc.), and that it does not matter if a container is destroyed as long as you can make a new one to transfer its contents into. I completely disagree with this approach. Utility is valuable because people are valuable, not the other way around. A world with lower utility where less people have died is better than a world of higher utility with more death.