You make a good case, but I feel it's within the realm of possibility to create emotional impact even with characters you don't really spend a lot of time with. My main example of this would be the introduction to The Last of Us and Joel's daughter. I'm very doubtful that the wife and kid are going to be put on the slab that early (if at all) in the game.

For some, the wife won't be put on a slab at all, and will be the one stumbling dazed out of Vault 111 unaware that over 200 years have passed.

That too.