Also there's a huge difference between our current culture and the medieval one where GoT takes place.

Jon isn't just a step-child. He's a bastard step-child born of (as far as Cat knows) a tavern wench. So not only is it conscious decision vs dragging home a kid after you're married, it's actually conscious decision vs dragging home a kid after you're married who is ALSO a commoner who is ALSO a potential threat to the inheritance of your own children AKA the whole reason women were married off back then.