Mainly heartbreak. The scene is setup such that the character would believe the child is Shaun at first. Then Father steps in and unloads the truth, shutdown code emphasizing the point... at least the truth is something, but utterly heartbreaking. Synth Shaun isn't the real Shaun at all, and is already fully indoctrinated by Father anyway, so there is little hope of say, stealing synth Shaun and trying to raise him. He'd just be a kidnapped child at that point and would never really be able to trust the player or let go of Father. Father is too old to really develop a mother/son relationship with. He's already lived a full life and there isn't much that can be done to turn him around. There might be some shred of good in him, but it's too little, too late. The sheer truth of the situation is that there is no saving Shaun. ((from all I've encountered so far anyway... maybe there is more of this synth Shaun story than what I've encountered yet))
I see some vague hope that a Shaun clone could be made to sort of replace Shaun, but that memory will always be there of the loss. It would be better, cleaner, to just move on.... perhaps start a new family... or just decide to not to have a family and make the Commonwealth your family. A life dedicated to building a safe, properous nation would be a life well spent. As things are now, who'd even want to have a child in that mess?
Of course, I also have 7 vials of immortality serum from another questline and an incredible array of contacts with various extraordinary skills. I don't think mortality will be a limit for this character. I expect that after a relatively safe and prosperous nation has developed, the idea of a child might be start looking more practical.