Most reasonable people anticipated a minimum price of $400 for the system, so an increase of $50 is not insane, especially considering that the new system features a larger screen and bigger battery, all of which can significantly increase production costs. Additionally, the specifications suggest that it is more future-proof than the original model (although this is speculation) and obviously, high inflation.
The software pricing strategy is a more complex issue. Historically, Nintendo has opted to sell hardware at lower prices while generating profits through software sales, in contrast to Apple, which has traditionally sold higher-priced hardware but provided free access to its software. I have noticed that this crucial aspect is often overlooked: how many of the games for the original NS, as well as the development of the new system, were financed by top-selling titles like Zelda: BOTW and Mario Kart 8? Nintendo does not calculate game prices based solely on development costs divided by unit sales; instead, they consider all their major titles as evergreen products that sustain the company. For instance, the revenue from MKW can help fund future projects such as Bayonetta, Pikmin, Xenoblade, and even Metroid, not to mention other R&D expenses.
(I also believe the higher price of Mario Kart World is intended to make the bundle more appealing.)
I think the biggest factor is that we have become accustomed to Steam sales that reduces prices to ridiculous levels and to $20 indie games that are just as good as any other top game. Additionally, there are now countless options available, along with a vast back catalog of games that are affordable to play.
To finish, how do you determine the price of software? Is it based on the break-even point for development, or is it a fixed price of $60 for AAA titles? Games like CoD, AC, and various sports games consistently retail for $60, often supplemented by micro-transactions. Given their sales figures, these titles could be priced lower and still be profitable. It is almost hilarious that they are sold at the same price point as titles like Metal Gear Solid, Witcher 3, and Elden Ring. Same story with Nintendo, would you be willing to pay $60 for Breath of the Wild, Mario Odyssey, and Smash, or for Pokémon Sword, Advance Wars, and Princess Peach: Showtime? It is often stated that video games provide the best 'price per hour' entertainment, and I believe this remains true today.
I also recommend watching this video from three years ago for some humor and perspective on the topic: