Bows of the Native Americans were most definitely kept unstrung in most cases. There are many accounts of Native Americans doing just that, including with a reason given (sparing the bow from excessive strain), as well as the fact that the majority of NA bows have strings that have a fixed end and a noose end. Even the one-sided nocks favored in the Plains are so to make unstringing and stringing a bow easier. It works, too.
Low brace heights have already been discussed at length, and good reasons given. More cast, more durability are my reasons to use them. I shoot mostly 50" selfbows these days, with a 20 - 22" draw. My favored brace height with these is around 4 1/2", measured from the bow back. That's less than a palm width between bow belly and string. My short bow arrows are cut to drawlength, so they have no "overhang" at full draw. Also, I mostly use D-style bows, with the full width of the bow at the arrow pass. I have no issues getting perfect arrow flight with these, although I had to test lots of spine and point combos to find the right ones for this setup. You only have to do this once, and any Native American would have had pertinent insider knowhow to start with. Heavy arrowheads, as common on the Plains, help tremendously in getting clean flight and plenty of penetration without much length anywhere in the setup.
There is no bow style that was quicker and easier to make, starting from acquiring the raw materials, through roughing out, tillering and even stringmaking, than a short, narrow, bend-through the handle bow. It is a highly efficient weapon in this regard.
Tuukka