I think this is already in the game actually, I saw an example where they actually did forget their hat, and this was confirmed when you called the residence.
I'd really like a version where you immediately die after letting in a doppelganger, otherwise it's difficult to know exactly what I did wrong even with the details.
Absolutely amazing, and if you were wondering, no, you're not the only one who'd love to see something like this. I would pay good money to see this happen.
Maybe after 10 "captures" during the c o o m scene an egg fertilization scene plays? Could be disabled in the currently just for show options tab for those who aren't into that sort of thing.