The point is that you can exhaustively explore the space without logarithmic overhead. There's no benefits to doing it with random sampling and it doesn't even save thought.

In my experience it is fairly easy to randomly generate a valid object but very difficult to write an algorithm that exhaustively searches the space of all possible objects, and usually not tractable anyway. The space is usually too big to exhaustively search.

I already explained what the benefit is. What is it with this focus on offloading work from computers to people? Let people do things more easily without thinking, even if it burns more increasingly cheap cycles.