Bruce Hood, Chair in Developmental Psychology at the University of Bristol, has an answer--though not of the typical variety--in his Psychology Today article, "Why Do We Need a Brain?"
However, keeping you alive is not the sole responsibility of the brain. The same could also be said of your other major organs including the heart, liver and lungs. While it is true that these can all be successfully transplanted whereas a brain transplant is neither possible nor desirable (the topic of forthcoming blogs), it is not the case that to be alive depends on having a brain. There are many animals that are alive that do not have brains. They may have simple nervous systems but they do not have brains as such. There are even some animals that start off with a brain that they later discard. The classic example is the sea squirt that begins life as a tadpole-like creature, swimming around the ocean in search of a suitable rock upon which to attach. It has a simple nervous system to coordinate movements and even a rudimentary eye spot to “see,” but when it finally attaches to the rock, it no longer needs to move around and so digests its own nervous system.
Read the entire piece at Psychology Today.