Actually, the big lesson to learn from PS4 is that consumers will accept an $800 console as long as you mask it with a pricing system that has $400 up front and then $50 a year for as long as you own it.  In the past Nintendo has sold hardare at a profit because it needs to, as it is a games company.  Sony (and MS) was OK with losing money on Playstation because it isn't really a games company.  If DVD or Bluray took off, the system did its job.  But now Sony is in a financially precarious posistion, and Kaz set forth that Playstation needed to be a pillar of the organization and make money.  And with consumers willing to accept the subscription model, it is now possible to sell hardware that is both powerful and making a profit.  This is the trend Nintendo missed out on, badly.

Nintendo should have made a more powerful system, made games that used online heavily and charged for online.  They could have had a system that 3rd parties would support, consumers would want and they could make money on.

Going forward, Nintendo must learn this lesson and join this trend.  ASAP.

Agree with that. I would just add that the strategy in your second paragraph (that's is in my point of view the correct one for them) needs one more thing: restore broken relations with 3rd parties. I believe they should work with 3rd parties since the begining of the hardware project (as Sony and MS did this gen) to make sure they will get support, or they can end with a more expensive and powerful unit without the games to use it. 

And the biggest part of it is that Nintendo wouldn't need to really lose what maked them Nintendo. They are defined by their games, gameplay style and level design. For me, Wii and Wii U were out of Nintendo's style, they were gimmick consoles. SNES, arguably their best one, didn't had any gimmmick and was the most powerful one with heavy 3rd party support. For me, N64 was their best and it would have competed a lot better with PS1 if they didn't used cartridges and allowed a 1.5 year head start. It could appeal to children (Pokemon, Mario), adults (Goldeneye, Conquer's) or both (Zelda Majora's Mask). 

That will only happen if they change their corporative culture ("do what we want, ignore the others"). I believe Iwata must go and they should bring an external CEO (like BlackBerry did with Chen), with a different perspective and work style. Could be an internal guy to, if he isn't like Iwata. Kaz on Sony is an example, Kutaragi believed SCE could do anything and sell premium priced products and everyone would buy because they wrote PlayStation on it. Kaz changed everything with PS4. That kind of culture shock is what a company needs after a struggling product. And they need to change ASAP, before Iwata start defining their 9th gen machine. And even on this gen, a new CEO could start to rebuild relations with 3rd parties to, at least, gather some support for Wii U and prepare them for what's next.

Absolutely they need to work with 3rd parties.  Either that or buy them, and working with them is likely the much cheaper option.  In the past "working with" third parties would mean selling hardware at a loss to please them.  But now with online subscriptions Nintendo could sell the system at a loss but make it back up with subscriptions.  They made massive profits by making $49 per Wii.  If they sold a kick-ass system at $399 (the same price as NES, adjusted for inflation) with $450 worth of stuff in side but an annual fee of $49 per year, they would have Wii level profits within 2 years of ownership, and a system on par with Sony and MS.  They really, really need to work with 3rd parties and get them on board.

And yes, the SNES was truly Nintendo at its best.

Eh. I think they can hold their own. As I've said many times on these forums, the Wii model is too risky. It worked the first time but it failed the second time. Without the right marketing, right gimmick, right price, and right games, the whole thing falls apart like the house of cards it is. If they release a system on par with the PS5 & Xbox 4, while they may not "win," at the very least it'll be guaranteed to sell a whole lot better than the Wii U because they'd have a system that third parties would actually want to develop their biggest and best games for. Nintendo got lucky with they Wii. They don't need "lucky," they don't need to make another risky innovation (assuming there's really anything left to innovate, and most of the more recent "innovations" are really tech that was already years or decades old). They need to play it safe next time.