Nintendo shouldn't go 3rd party and here's why
In this example let's say Mario kart 8 sold 3 million units on the Wii u and made 500,000 people buy Wii u's. After making $180,000,000 off of mk8 and 150,000,000 off of hardware their profits would be 330,000,000. Let's say mk8 was on ps4, xb1 and PC and it moved 5,000,000 units they would come up short with only 300,000,000 in profits. Nintendo wouldn't see their typical profits because the audience for their games is primary on their consoles and without those people buying their systems that's a huge chunk of revenue gone. And the mobile market is out of the question. Mobile games thrive based on cheap entry prices and micro transactions. Nintendo could never get away with charging $20+ for iPhone games so unless all they make is games like Pokemon shuffle that is not a viable market for them
Your example doesn't work mathematically. If they sold 3 million copies of the game they would only get about $102,000,000 (retailer share, distribution cost etc come out of it). Then if they sold 500k Wii U's, well actually I think they still make a loss on every Wii U sold, even if they don't the profit margin is very small. Let's just say they make $0 from that in case they don't make a loss anymore (first few years definitely did though).
Now on the other side, 5 million copies as a 3rd party would make them $135,000,000 (same expenses as above + platform royalties)
Source for breakdown of sales revenue http://static.giantbomb.com/uploads/original/3/38417/2368348-1289873-gameanatomy_super.jpg
So Mario Kart 1st party release = $102m profit
Mario Kart 3rd party release = $135m profit
Therefore going 3rd party would increase profit by $33m
Of course, it isn't as simple as this and there are many other factors to consider such as the money they make in platform royalties on 2nd/3rd party games and of course how it would affect smaller games that don't sell as much as MK. But still, it disproves your example.