Nice argument! And to clarify further, the equivalent implementation for `random(random())` could be viewed as a rejection-sampling implementation of random(random()).

Another intuitive rephrasing is that while both min(random(), random()) and random(random()) are guaranteed to be at most your first draw, with random(random()) your second draw is constrained to be within the interval of your first, whereas with min(random(), random()) there's no such constraint on the second draw. Thinking about P(x > y); x,y~U should then provide the illumination.