It has higher energy density than Lithium, so theoretically yes it could increase the battery life of your phone. For equivalent energy the size is 33%, so one could fit 3x the energy capacity into a cell of the same size.
The real reason is that if you make several million phones that a certain percentage is always going to explode, either by manufacturing defect or a user pierces the cell through accident. This might mean the difference between some light leg burns or your death and phone makers are not going to take the negative press of the latter scenario. Their only answer is better power usage.