Fearing death is not a choice. It's a reaction, and an involuntary one. The real question is do we have the will, and should we exert the will, to overcome our fear of death? To answer this, we must additionally ask if there is anything beneficial in the fear of death? Because if the fear of death doesn't deliver some benefit, it is worthless to us. Even a hindrance.
From a social perspective, the fear of death is important. It's one of the ways the system keeps us in line. We don't want to die, so we obey the system which can kill us--often with the blessing of the law.
But from an individual perspective, fear is a weakness. Literally. The fear impulse from the amygdala is also accompanied by a corresponding decrease of activity in our frontal lobes--the seat of our reason. Fear makes us stupid and slow to act. The successful organism is the organism that suppresses that fear impulse and stimulates the reasoning brain into action. The fear impulse isn't even needed in order to get that reasoning brain going.
So, as far as the individual is concerned, fear is only ever a negative condition. That includes fear of death.
In Hindu philosophy, fear of death is included as one of the kleshas--poisons of the mind. It is a barrier between the mind and the liberation of the mind. An agent of the false duality of "life and death." It prevents us from understanding the universe as an absolute instead of a mechanism of differentiated parts.
We developed our fear of death as we evolved into thinking beings. Unlike the lower animals, human can conceive of things we have yet to do. We desire to do these things because we anticipate they will bring us joy. Therefore, we fear the event in which our time runs out and we can no longer do them. This is a manifestation of yet another klesha--the attachment. We develop attachments to unfulfilled desires.
The kleshas often work in unison. Fear, attachment, ignorance, ego. All working against the individual and the mind. Working against our reason and logic. And yet, we can't let them go for one reason or another. Sometimes we even defend their existence by making statements like "we need fear to survive" or "ignorance is bliss." We are klesha junkies making excuses for our habits.
Fear of death is only necessary because we don't have the strength to let it go.