The video isn't supposed to be a proof that no technique can do it; the video just demonstrates that soap bubbles can get stuck in a local minimum.
(Also, blowing is not guaranteed to move the answer towards the global solution. Even if you can quickly determine that an answer is not optimal and blow it around, you could just spend forever going in circles.)
(Also, blowing is not guaranteed to move the answer towards the global solution. Even if you can quickly determine that an answer is not optimal and blow it around, you could just spend forever going in circles.)