I'll offer one possibility for why this was done in Fallout 4.
How do you get the player to care about Shawn?
We see him as a cute baby and spin his rocket ship mobile and that is about all that is possible with him being just a few months old new born.
Not much of a story if the player isn't invested in finding out what happened to his family.
But what if we are also shown Shawn's mom or dad, our other half in this baby.
We can see their love for Shawn, we can look at Shawn and see his resemblance to both of us, it makes him more real.
Even more so, if our spouse dies leaving Shawn alone.
It brings the war home if you know you have lost your spouse forever and you might never even find out what happened to Shawn, let alone actually see him again.
If yesterday you were in your happy pre war suburban home with your spouse and son and today you are all alone in a nuclear wasteland.
And you have been shown what your pre war life looked like and you can see it is nothing but ruins now.
Wouldn't you want to do right by your spouse and find and protect that last link to your pre war life?
I expect this to be a major quest, but personally think it won't be totally tied in to the main quest.
You will be able to ignore it if you so chose.
There is a lot Bethesda could do with a story line like this.
Even if it is just a reversal of the Fallout 3 child looking for his or her father.
If nothing else I figure developers look back at previous games and say you know we can really do this MUCH better this time if...