Why can't I use sand as grit after all thats what the ocean uses. Okay, so the Ocean perhaps the biggest open barrel tumbler in the world uses sand. And through the millenia it works. You on the other hand have limited time. So here is the reason you buy grit. Its harder than sand.
Compare the relative hardness of sand and grit on a 10 point scale. Sand is 6 and Silicon carbide is 9+ on the Mohs hardness scale. And Mohs knows.