I know sweating isn't perfect, for the reasons you mentioned, but do we see nature evolving any better solutions at a mammalian level?
My armchair understanding is sweating is a natural marvel with nothing else like it seen in creatures as large as us. That it truly is a differentiator between humans and other animals (or mammals at least). Sweating is the foundation of humans ability to engage in long-distance endurance running which is one of our unique features, also called persistence hunting[0]. You can easily draw a line between this sweating and our ability to travel large distances and hunt the way we did, which in turn can be connected to humanity's success as a species on earth.