Can't really agree with much of what's said about the 3DS here. I think the misread on the 2DS is especially big. But to get back to the salient point:
Nintendo doesn't know. They have to weigh the risk of overshooting against the risk of undershooting, because they don't have an oracle to tell them the perfect intersection between appeal and price. Saying "price doesn't matter, as long as you make it worth the price" is just an oxymoron.
So if you aim low, what do you risk? Your margins may end up slimmer than what you could have gotten away with -- something you can never be sure of anyway -- but as long as you're not losing money, you're still profiting and building the install base where you can focus on evergreens and attach rate, as Nintendo does best. And then you never have to cut the price!
The Switch dispositively shows Nintendo following that logic. It's basically the Wii U gamepad with the rest of the Wii U stuffed inside it and then some, and yet it costs the same as the Wii U did. $50 less than the launch price of the model with the same storage capacity, before accounting for inflation. They very clearly didn't decide the price based on the maximum they could get away with. They erred on the conservative side.* And I will acknowledge that they were in a much riskier position in 2016 than they are today, but I find it highly implausible that just because the next model's launch isn't as do-or-die, they're going to do anything differently from the safe and demonstrably lucrative strategy they've been doing. Take the differing situation in 2016 vs. now, add to it inflation and uncertainty, and yep, you likely get a significantly increased price -- but not a price without a ceiling.
*Again, not the same thing as aiming for cheapness because I think cheapness sells or whatever.