It is safe to take baths using untreated water because uranium or radium is not absorbed through your skin. A distillation system works by boiling water into water vapor, then returning it to its liquid state. The minerals and contaminants such as uranium form scales and are trapped in the boiling chamber.
Starting with Uranium. Full energy release means no wasted fuel at the end, which eliminates the problem of longlived nuclear waste. Of course, such a reactor must be efficient at the chemical recycling step, which is a strong reason why reactors that use liquid fluoride .