This isn't an actual solution. Video Games have to do things fast. You can't just sit there and wait for a minute as you try brownian motion on hundreds of units. There are plenty of different solutions to get more realistic and natural pathfinding, typically navmeshes and then local node based movement. But you still need to go from a to b, somehow.
Your example also fails in several really obvious ways. What if there is a pool of mud or water in the middle of the path, it IS traversable but doing so is not ideal? A* you give this a high traversal cost and you'll naturally path around it. Your solution will have the object going through high cost but traversable areas in strange ways. This is going to be worse, as players will just kite and exploit this fact.
Your example also fails in several really obvious ways. What if there is a pool of mud or water in the middle of the path, it IS traversable but doing so is not ideal? A* you give this a high traversal cost and you'll naturally path around it. Your solution will have the object going through high cost but traversable areas in strange ways. This is going to be worse, as players will just kite and exploit this fact.