Yes, our bodies have a specialized method for removing "old water" so it can be replaced by the fresh water one intakes. Urination. Your kidneys are working day and night to dump those "things in it that you would rather have not in your body" into your urine - not your sweat.
Animals that sweat are a minority. The idea that there are toxins that can only be collected and removed and by your sweat glands, instead of your kidneys, should be treated with suspicion.
I would also like to point out that even if one can detect the "presence of toxins" in sweat, however that is defined, it is not proof that sweat is an effective, efficient, or primary vector of their removal - it only proves that those toxins permeating your body happen to leach into your sweat. The rest of your body could either be removing 10000x as much of the same toxin every time you urinate compared to an hour of sweating, and the sweat could just have some insignificant dregs that happened to leach in - or there could be 100000x as much of the toxin remaining in your body no matter how much you sweat, either diffuse or concentrated in some non-sweat-gland-adjacent organs, making their removal through sweat completely ineffective.
Animals that sweat are a minority. The idea that there are toxins that can only be collected and removed and by your sweat glands, instead of your kidneys, should be treated with suspicion.
I would also like to point out that even if one can detect the "presence of toxins" in sweat, however that is defined, it is not proof that sweat is an effective, efficient, or primary vector of their removal - it only proves that those toxins permeating your body happen to leach into your sweat. The rest of your body could either be removing 10000x as much of the same toxin every time you urinate compared to an hour of sweating, and the sweat could just have some insignificant dregs that happened to leach in - or there could be 100000x as much of the toxin remaining in your body no matter how much you sweat, either diffuse or concentrated in some non-sweat-gland-adjacent organs, making their removal through sweat completely ineffective.