Nintendo will not go mobile. It's never going to happen. It would kill the company, despite it being what several short-sighted investors may want.
Iwata leaving is a possibility, but I also believe it'll be detrimental to the company. This isn't America where if something goes awry, then you should fire the guy who did it. Iwata built a lot of good will off of the DS, Wii and subsequent turnaround of the 3DS. The Wii U is a different beast with a lot of issues (even though I feel it is actually the best console out right now).
People continually believe that removing Iwata would magically fix everything when it could, and is more likely to, make things worse. First, Iwata isn't responsible for every decision. Yes, he's the CEO, but anyone in business knows that the CEO isn't responsible for every damned decision, that it's a group thing with the board and that if you want radical change, you'd have to completely clear house. The likelihood is that any replacements would be akin to Sony and Microsoft's heads and them not be gamers, but just focus on making quick money. Sure, Sony has Cerny to help steer them hardware wise, but if they didn't, they'd almost certainly have gone the same route as Microsoft did.
Nintendo as a company is one that doesn't wish to screw the consumer. Iwata was put forward the idea of microtransactions in Animal Crossing and shot it down instantly due to it being a horrific idea, even if it would have made them money. They don't allow their games to have DLC that completes the story or is locked away on cartridge. They delay games until they are perfect, rather than rush them out and just "patch it later". Do we really want this clearly gaming company to go the way of all the others?
Is Nintendo in trouble? Not really. They're back in the black now, despite operating profits still being negative, but that's explainable a fair bit. Do they need to shake things up and invest? They have been in the last year. There has been a major reshuffle of the higher ups of Nintendo and their HUGE R&D building is just about finished. This building drained a lot of their finances.
Is Wii U in trouble? Yes, absolutely. However, the Wii U is not everything Nintendo. It does make a dent in its financials, but the other avenues of Nintendo DO help prop it up.
Now, let's assume Nintendo go third party. People assume everything will be fine. However, they will lose their hardware streams. They will have to restructure and downsize (after building the big building meaning it was a waste). Output would diminish in both quality and quantity (Yes, they actually do release a lot. Rather than say "lol it has no games, actually look it up). Employee morale would diminish which would have an impact on their work. As the games would be the sole financial avenue, the software output would be their only way of getting money. Gone would be the times of experimental games like The Wonderful 101, and smaller franchises like Steel Diver, Kid Icarus, StarFox and even Metroid (It doesn't sell...get over it). It would become an annualised company of Mario, Pokémon, the occasional Zelda and Pokémon. It would then kill the company.
Same if they went mobile, especially as Nintendo's games require split second accurate control which just isn't very feasible on smartphones due to how the touchscreens work and the different architectures preventing a standard. It'd diminish quality.
Why not allow me to cultivate online friendships in a console format as well?
This is not a one or the other argument...It is a why the fuck not both argument!
It is both. Hence why Pokémon X & Y is on the 3DS, which can be portable and online. Putting it on a home console would remove the portable aspect and thus it isn't "both", but is the lesser.
The idea that Pokémon doesn't need to be portable is one perpetuated by players in the west. There is a massive cultural divide between Pokémon players in the west and those in Japan.
In the west, people buy the games, occasionally play with their friends locally, but focus on online. If there's an event distribution, they may go, but they will more likely sit in the car park and download the Pokémon there.
In Japan, however, if there's an event, there are massive queues to get into it. People battle, trade, do Funfest Missions (Gen V), help eachother with O Powers and loads.
Just recently in Japan there was a Gengar & Scizor event in Toys 'R' Us and Pokémon Centers. It was more popular than they could have possibly imagined that they had to post an additional note on the official site about the time restrictions and removing other barriers for getting the Pokémon.
Pokémon is quite clearly a handheld franchise. You say why not both? It has both. Putting it on a home console would just kill a large part of the market without giving any actual benefits other than "Look, pretty graphics".