Kimishima already said there should be 3DS successor, as an affordable portable for children. I think the word choice is important here too. Nintendo has this stigma of being kiddy. With the Switch reveal and following ads, they presented the Switch as aimed at adults, and the high price actually helps with positioning it as such. They want to get rid of the kiddy image and this notion of Switch = for adults, 3DS and its successor = for kids, will help to provide an alternative narrative.
In regards to price, I think with the Switch, Nintendo released their XL version first this time. The DS iterations all featured XL versions at some point, and they all sold better than the smaller versions. With the New 3DS, XL and standard size were released at the same time and both models sold well, but the XL sold better.
So it's nice that users don't have to buy a small unit first and rebuy the big one they always wanted later. Still, some might prefer a smaller unit for higher portability or because they want to save money. In fact, one of the main and more plausible reasons cited why the Switch might fail was the unprecedented high price. Now that it's out, that doesn't seem to be problem really, but the additional model can still reach more customers who think the Switch is too pricy or too big.
In my interpretation, the 3DS successor wouldn't necessarily be called Switch at all, but it should play the same software as the Switch, because the whole point of the hybrid was to unify software development and not spread efforts between two architectures anymore. Of course, if it gets a different name, it won't be possible to lump sales of the two devices together and the divided sales might not be enough to become number one. On the other hand, both models still each should outsell the whole Xbox1 family and it's not impossible that one might outsell the PS4 family in the long run.
Remember that rumor from 4chan, calling the NX Focus? It already acknowledged the hybrid nature but made this strange explanation that you could focus on portable gaming at a time, or on TV gaming at a time, and it made little sense. Switch much better captures the concept. But Focus would be perfect for a Switch variant that only does one thing, like a Focus Portable or a Focus TV.
Since it will be the true 3DS successor, they might make it more like the DS series. Maybe just one detachable controller* that connects to the bottom of the main unit, which should also be screen only, little to no bezel. Same clam shell design as DS line, and the controller could also be used as a stand, with the user holding JoyCons they got from their Switch or bought seperately.
It could be backwards compatible to 3DS, via emulation. The main reason why Switch doesn't and probably shouldn't feature 3DS emulation at this point is that they still want to sell 2/3DS hardware until those are actually discontinued. With a true successor launching, that won't be necessary anymore.
The smaller model could even feature a parallax screen for stereo 3D. Mainly for bc games but maybe also some Focus Portable exclusive games. 3DS emulation and those 'exclusive' games could also come to the regular Switch, playable on a 3DTV. 3D would give owners of a Switch who are content with their purchase a reason to still get the Focus (3D?), because it adds something they don't already have. For users that don't care, it won't be too expensive and they can just ignore it.
~$300 Switch, ~$200 Focus. It makes sense.
*BTW, I think detachable controllers will be what Sony copies from Switch with their Vita successor. There will be one.
