Based on the original question, I thought we were discussing Plains Indians, or at least the NA of Western North America, not the uttermost reaches of South America, but hey, it's all good!
Photos are always a bit specious, since there is no way to know how much setting up was involved, then as now. Strung bows look much better, or are simply much more identifiable than unstrung ones. When it comes to the Selknam in your first photo, the definitive ethnography by Lucas Bridges (who grew up and lived among the Selknam at the turn of the century) specifies that the bowstring was carried inside a bladder bag and put to the bow at the last moment, to protect it from the wet weather that made it useless. The extremely unpredictable and wet climate of Tierra del Fuego had an effect here.
I have studied a set of Selknam bow, arrows and quiver (fascinating stuff), and the upper end of the sinew bowstring had a running noose, easily separated from the nock, plus clear wear on the string end over some distance, most easily explained by repeated stringing and unstringing of the bow.
Always-strung bows can be found, for instance, in the Amazonas, where extremely low brace heights and extremely long bows are common.
Back to North America, the Yuma are a special case, using intentionally deflexed willow & cottonwood bows that are under no strain when strung. Even then, a Yuman speaking Paipai elder kept his willow bows lightly strung when not in use and tightened the string before using the bow, as described by Paul Campbell (1999).
8 - 10 hours of continuous strung time is no biggie even these days. I'm often out in the woods that long, strung bow in hand, as is every hunting / 3D-shooting archer I know.
Tuukka