I've never thought that the traditional format of repetitions and sets is very "natural". For one, no other animal besides us lifts weights in such a structured fashion. And this current version of weightlifting has really only gained popularity in the last fifty years, so it is a relatively recent phenomenon.
I'm not denying that modern resistance training works to build muscle and improve performance. But I do doubt that hunter-gatherers performed anything close to this type of weightlifting.
I've been reading this paper that suggests that load-carrying was a determining factor in how the human body developed. The paper mentions that hunting activity can be divided into three categories: capture, processing, and transport of game and tools. The authors then go on to point out some anatomical features which suggest that carrying was a significant factor for human body development.
A modern equivalent of this type of load-carrying is the "farmer's walk", where a person simply walks while carrying a heavy weight. I used to do these in the past but I have gotten anyway from them in recent years. This research has made me think that this type of lifting may be more "natural" and beneficial than modern lifting programs.