They do not NEED to be there. But let me tell you a story.
When my son was born I was in the room. As you might have supposed my wife was also in the room. The experience was indescribable. When my son was presented to the world and o was asked to cut the cord it was truly a life changing experience. It allowed me to me involved in literally every moment of his life.
He was born perfect but not without some real effort. We held him and fell in love instantly (and again and again since).
Both my wife and I were amazed and honored that his beautiful and courageous birth mother allowed us to experience his birth. It created a bond that we will all share forever. He is ours. He is hers. He is amazing.
Of course some dads cannot be there. I actually filled the role for a friend's wife as he was deployed elsewhere in the military. My wife actually experienced this in another instance when a friend had no other person close enough to share the moment.
It is scary. It is kind of gross. It is life in its most pure form. If you ever get the chance do not shy away from it. Embrace it as an opportunity to share in something that has gone on since the evolution of our species. It ties you to every other human since every other human was also born.
Be brave. Be proud. Be there.