In the case of Fallout 4, the big deal is that if you were a synth, that means all your memories and experiences prior to a certain point of your existence are almost assuredly made up. They are a fabrication. Maybe you never actually lived in the pre-war era. You never had a wife. You never had a child.

It would have been better from a story-telling point if that wasn't added in a DLC long after most people played the main game through. It fits better if you do Far Harbour before ever finding Shaun so that you are forced to wonder if Shaun is even real.