But the relationship between population growth and technological growth seems fairly clear.
In either case, whether technological growth happens or not is irrelevant. It's not worth billions of lives. Nothing is.
> Wouldn't this mean that within few generations there would be no more kids, as sooner or later each genealogical line will end with an individual who decides to live forever?
Sure. And that would be a choice. I see no issue with this scenario.
> Acceptable by whom?
Consider a society in which everyone lives forever. You start saying that they should all start slowly dying for the sake of progress, that they likely won't even be around to see.
You'd be regarded as somewhat crazy. We shouldn't have to have (billions of) people die to accomplish our goals. That's like trying to hammer in a nail with a meteoroid.