I'm sure there have been many Professionals in the history of life that have both missed and been there for the birth of a child. All depends on circumstances, so I would hate to say that there is any clear cut formula for this. The Packers circumstances, open roster position, allowed them to look like the caring organization. For all we know, Scott said "use my pay and whatever else I need to kick in to cover my replacement." I am guessing most of his teammates supported the Packers putting Family over Football, which could go a long way for team unity and character building. Ultimately, Scott was provided with the decision to make, I doubt the Packers said "you are not playing, go be with your wife."
Side note, if I am an NFL player and planning a family, I'm only "practicing" when the timing of giving birth would be during the season. Take the helmet off and go for it when the birth would happen during the off season.