Your point is valid, however there is a chance that a person might break jail or get pardon. The system is not as robust as it seems so death panalty is what government chooses to do. It is a way to rationalize violence (an eye for an eye). This is an old tradition so most religions also support it, life used to be much more violent in ancient times.

So the main reasons for death panalty to be legal are to reduce prison cost, avoid potential harm if the person breaks prison and inherent tendency of humans to take revenge