"children grew up more attached to their robot nannies than to their actual parents. This was mitigated by making the robot nannies somewhat severe"
This reflects a very simplistic view on who kids love. It is in fact wrong even in the first order: kids actually love more severe parents or severe teachers (obviously, below a severity threshold, I am not talking about sadistic education here).
I experienced it myself as a kid: we respected and loved much more the teacher of French litterature, because he was severe and knew how to make himself respected. The German teacher tought the softer she was the better, and she was bullied and hated.
I experienced it with my own kids, and with the kids of friends. Each time I am severe with them, e.g. not bending to their will, I gain points in their hearts.
If I were to find a way to make kids prefer their parents over their robot nannies, I'd say we would just let the parents have and show they have the power of decision, and therefore the power of empowerment. From my experience kids love the most those would can empower them doing new things, the ones who will forbid and allow. a personal example is thusly: I forbid my 4yo son to touch my tools, but he is allowed to watch when I'm fixing something, and sometime I ask him for help ("bring me the screwdriver") and he is sometime allowed to use some tools when it is safe and supervised. This is I think a great way to make him interested in tools, and to feel empowered when he can use the usually forbidden screwdriver, and he clearly loves it.