Yes I would because there wouldn't be any reason left for me to own consoles.

They would not have more resources because they would lose all the licensing fees from their platforms. Time? Really? The hardware engineers they employ would have more time making software? lol.

Would I mind? Absolutely, I'd hate it so much that I'd never buy another new video game again. You said that this would just be the home console and handhelds would be a different story, but they are inseperable. If you have Nintendo franchises on opposing consoles, but then still have the Nintendo handheld, the handheld would die even worse than the Wii U has. There would be no incentive to buy one, this is one of the worst ideas I've ever heard, quite honestly.

There are... More problems than you can see...

Lets say that Nintendo suddenly goes third party. Than Nintendo actually gets more leverage on the console market.

For example, lets imagine the scenario where Nintendo suddenly declares that all of their home console title will be third party, and will only release on Xbox One.

This declaration, if it would happen, would rearrange current generation. Xbox One will quickly catch and possibly surpass PS4 because - well. All the Nintendo's current share will move with them, including additional share who wasn't sure Wii U would be a good deal.

Problem is that Nintendo have no reason to support Western console that is selling less and going to ignore them.

If Nintendo sides with Playstation, Already struggling Xbox will probably have to bite the dust.

That would result in single console dominated market without healthy competition.

Well, that is my take.

Without having to sell systems,Nintendo would have no reason to diversify their games, and would probably just make the games that would make them money.

Sega is kind of a bad example even though it's the only console maker to go 3rd party. They're bad with money. Nintendo on the other hand isn't. If nintendo went 3rd, what games get sequels or what gets released largely depends on the people who buy nintendo's games. Nintendo's loyal fans is it's only market amongst gamers and it's games reflect their tastes. If nintendo fans start to demand things then most likely nintendo will have no choice but to cave in.  At some point, someone has to say "this shit isn't acceptable" or "we want this game". Nintendo has never been in a position that it can just ignore it's fans because they are it's target consumers. 

-----> Nintendo dont seem like a hardware company.

They often dont see the future of hardware, or make gigantic design mistakes when it comes to hardware.
Their OS is lacking behinde competitors too. Then their overall design philosophy with "low power" & "quiet" console doesnt appear to be what the market wants.

Basically I think they would be better off as a pure software company, that just focus's on makeing games.

EIther that or they hire a guy like Mark Cerny to help them design the console, and some software guys to make a OS more like the others's.

That is doubtful. If Nintendo is a 3rd party publisher most likely, we'll end up not getting any of their fringe games anymore, because they just aren't gonna sell. You can say that Nintendo has no choice but to cave in, but most likely, like all 3rd party publishers, they'll instead focus on the franchises that do sell. Nintendo still has shareholders to appease after all. Or we'll see a couple of these games that may or may not be good, along with a warning from Nintendo saying that it needs to sell xxx millions if they want a sequel. Or even worse, a mega casual surge of their games on mobile and a complete abandonment of their fanbase.

Not only that their fanbase will most likely abandon them too. I don't know if you know this, but there is a certain pride in the Nintendo fanbase. Most of their fans will treat it as though Nintendo abandoned them. The reward for decades of loyalty is Nintendo telling them that the systems they bought are worthless and to go buy a PlayStation? They won't go after those games on other systems. Its why Wii U has some of the strongest attach rates. I'm hovering around 50 Wii U games. You wanna know how many games from Nintendo I'd buy if I had to get it on PlayStation? Maybe one. Maybe.

Did the 12 million Dreamcast owners buy millions of units of all Sega games on other systems after Sega shut down? No. They all went onto something else and Sega floundered. I should know. I was a diehard Sega fan from Genesis, Saturn, and Dreamcast days.

Yes. Believe it or not, some people actually like dual screen gaming. And Nintendo's UI. And free online. And controllers with the analog sticks and face buttons where they're supposed to be.

The op said they would stop making consoles but continue making handhelds, I'm explaining why I don't think that is feasible. Either they support their handheld 100% or they go full 3rd party.