It's one of the few things that I'd say you have to go through personally before you can have a balanced view. Though I have to say that, after being there for the birth of both my kids, I didn't get a warm 'what a miracle' glow and shed a lake full of tears, more of a relief that it was over for my wife as it looks rather painful, then a dawning and not entirely pleasant sensation of the level of responsibility I had for the rest of my life, especially with the first one.
I fail to see that being a footballer would make any difference, and a manager would be mad to say 'you have to play' to a player who asks to miss a game for this reason. Similarly with an actor in a play, which I think is a comparable profession. If your mind is elsewhere you won't be able to do these spectacularly unimportant jobs properly. Even more so if you are doing something with more consequences, like driving an ambulance or directing traffic.
Tricky decision for a player who will miss the Champions League or World Cup final for this reason though.