Think of every connection on the board as having two wires - the wire from the driver to the load, and the wire returning the ground.
Now, imagine the ground wire runs all over the place, in this spaghetti path, back to the driver. What happens to the inductance of that connection? What does the ground look like? Remember, electricity follows the path of least resistance. So is the ground return path at high frequencies going to be distributed evenly across all the copper and vias?
The vias minimize inductance of the return path.