TLDR: Any relationship requires effort and commitment from both sides. As your (future) child is too young to make the effort you need to do it on their behalf to start the relationship off, and they as well as your friends need to want to continue it when they get older.
Long answer: I don't think there is a norm. I am age mid-40s now so I have known friends have children for about 20 years, but I have no children of my own (unfortunately).
When a friend is expecting a child I always start off from a position of intending to keep the friendship going and have a relationship with their child too. I realise how much life shifts when you become a parent and I'm more than willing to make the extra effort to bridge that need as a good friend.
But as a consequence, I would say the friendships I've kept and the children I continue to take interest in and have some relationship with has largely resulted from how much interest the friend/parent has taken in me in return.
A few examples,
Friend only replies to messages to tell me how tired they are and have no free time, won't see me even if I offer to come to them and bring food for us with me - no relationship with them, no interest in child.
Friend will only see me when they have a "night off" because they know I am available to go out with, and then they want to go for drinks and only talk about how great it is to be out drinking instead of doing bathtime, shows no interest in me - no interest in child, little relationship with friend except for occasional night out if I feel like it.
Friend says they want to keep in touch and makes effort to show interest in me, but all conversation and meetings revolve around the child, think, "would really love to see you, can you join us at soft play" - some relationship with friend, very basic interest in child that ends when child is old enough to entertain themselves.
Friend genuinely wants to continue friendship and makes an effort to keep in touch and include me in their child's life, not as a babysitter or occasional present-giver, but as someone they value having around them and their children - these are the friendships I've maintained and value, and these are the children I've seen grow up and had a good relationship with from birth through childhood into teenage.