Hell, they could have tied that into the pre-war backstory even better. A small glimmer of hope of turning the wasteland around, harnessing everything they have done to help fix things. A chance at having your old life back, in some capacity.
They don’t even have to take out the dead spouse/missing kid plotline. Wake up after the last of the systems fail, oh shit, your wife/husband died during all this and your kids gone. Now you’re out in this new world, holding on to a pair of wedding bands as the last piece of your old happier life, lost, confused, and trying to find your way.
There’s still that element of “What happened while I was on ice? Is he still out there?”, could even still tie in to the Institute plot, without making the entire story ride on a rather unfulfilling reveal.
Of course, that would also work better if we could have an actual moment of “Even if Shaun is alive, would he remember me?”. Actually let the character deal with the fact that their child might very well be dead, or that they wouldn’t remember. That they would find an absolute stranger, one who’s been raised in this world, one who isn’t so caught up in “mother” or “father”.
“Can’t expect me to train my replacement if I don’t remember how I did it!”