The phrase, all life, has universal implications. If the Flood were only local, then God's promise of never sending a destructive Flood seems to have been broken. There have been other serious Floods in the world's history that have killed thousands of people. This includes the area of Mesopotamia. The rainbow, that God placed as a promise of no similar Flood, would be a meaningless promise.
"And I will remember my covenant, which is between me and you and every living creature of all flesh; and the waters shall no more become a flood to destroy all flesh."
Genesis 9:15