I'm trying to think of families with multiple kids I've known throughout the years. When it comes to handhelds, the perception is that it's owned by an individual. It's their Game Boy or their iPhone. These devices, by design, cannot be shared or utilized by more than one child at a time. It is realistic and expected that households would have one for each child. If you only buy one device for one child, the other is excluded. This necessitates each child having their own personal device to use and enjoy.
But I don't know about the Switch. It can be played on one television, or placed at a shared vantage point with the kickstand, and it comes with two controllers out of the box. The perception that a Switch can be shared easily, by design, tells me parents will buy one Switch for Christmas and not one for each child.
I don't think Switch numbers will be inflated by every child having their own, I think it will just be in every household (like the Wii). Even if it doesn't reach Wii-like sales, it can and will be immensely popular as a living room staple.