That stupid synth Shaun is nothing but a poor last ditch effort meant to make you feel bad for killing all of the insane scientist buried underground. It's stupid and inconsequential. And also contradictory to everything the Institute's stood for. Yet more great writing from Bethesda.
Okay, this is actually a big deal in Fallout 4's storyline and a major part of what passes for the emotional core of the story. Remember Fallout 3 and Daddy Lone Wanderer? Liam Neeson? Well, remember how he had this big dream about purifying the water in the Capital Wasteland? Yes, well, he decided that it was more important to look after his newborn son than it was to help thousands of people.
How does this relate?
I'm getting there.
The thing is, as much as there is a theme to Fallout 4, it is the difference between ideology and family/friendship. Arthur Maxson and Danse have a major dust-up over it because they're brothers in spirit if not blood yet Arthur's ideology says Danse has to die. The Minutemen's ideology was that, at the end of the day, they weren't able to stay together for their mission because of personal animosity. The Railroad has a die hard commitment to their ideology but end up betraying Patriot over it.
But the big thing is that all of the factions but the Institute want you to kick the Institute's ass and the only reason you're supposed to stick with the Institute is out of love for your son. Because, at the end of the day, there's no damn good reason to help the Institute but family causes spelled out in the game.
Still bear with me.
Shaun's entire storyline is that he's dying and this is causing him to be introspective. He's been the Institutes idealogical poster-boy for decades and their Kim Jong Il. However, now he's wondering about the road less travelled with his Father/Mother. So he creates the Little Robot BoyTM To see what it would be like to live a different life. He also awakens his sleeping parent/makes a Synth of them to murder Kellog because he has some weird idea of getting his parent revenge by proxy, even though Shaun could just send some Coursers after them.
Shaun's entire story is about him putting his personal family regrets over the Institute's greater good.