I agree we cannot make pregnancy "fair", for obvious biological reasons.
But we could make the situation when a women is pregnant more egalitarian for both parties. IMO your satire is not helping towards this goal; it just ridicules the male position.
> "Men will never risk their lives to give birth."
True. But it's also true that men sometimes risk their lives to protect the mothers and the children - and they always have.
Male sacrifices are somehow different from female sacrifices, but they are no less. Something most feminist choose to ignore.
> "That's why the satire works."
Your satire might works for self-centered women for whom "It's all about the woman" and like to bash men.
It isn't working for men; you're not getting any male to join your cause this way. :-/