Unrealistic? What about the fact a child will willingly be adopted by a stranger after a 1 minute conversation

?
That depends on the life circumstances of that child. Look at little Runa when you enter the orphanage, even in the vanilla game where the adoption mechanic doesn't exist. She begs you to adopt her. Why? She doesn't want to be a kid in an institution, even one run by a dedicated and caring person like Constance. She wants to be someone's daughter, pure and simple.
Remember that in these days of modern medicine, safe workplaces, and abortion on demand, we have relatively few parentless or unwanted children. If you want to be a foster or adoptive parent, you have to go through an exhaustive process of home studies, training, and God knows what else. Because we have far less need of them, orphanages are a rarity here, and the few remaining are strictly regulated by child welfare laws that don't exist in Skyrim. So know that an unwanted child may well be overjoyed to have anyone call them "son" or "daughter". Some, like Lucia, were called such once nad never thought they would be again. Others, like Samuel, never heard it at all. To put it another way, when you're drowning and someone throws you a rope, you don't worry about what kind of person threw it. You just grab it.
The only thing I personally find unrealistic is that you can kill a kid's parents and then adopt them. It couldn't have been hard to create a game mechanic where children of parents you'd killed, even ones at Honorhall, would refuse to speak to you.