> If people lived 10x longer than they do now, the birth rate would have to drop dramatically

And it would, if you knew you'd live that long most wouldn't tie themselves down with kids while they're still young, they'd wait much much longer and go out and live life.

As it stands now, if you don't have kids by the time you're 30 you risk not being able to have them at all and having to suffer though months of fertility treatments and such just to try.