I don't think this is practical because many men do not take their full paternity leave. For biological reasons alone, the woman needs to take more.
Then I won't notify the company when I've had a child. Simple as.
Don't consider going down the road of "you must declare what is happening in your private life to your private employer" as someone else did either, without at least considering what an absolute breach of privacy that would involve.
There are arguments to be made that this right _should_ exist, but since it doesn't currently its not a reason to stop mandatory leave
Women “need” to take more than zero days off. That’s true, at least in our modern conception of child rearing. Both parents should take at least two months off, especially in the current system where people don’t have much community or family support.