I think Nintendo's mistake was that they were relying on third parties to fill in the gap for the wiiU. When we saw the wiiU's e3, Nintendo told everyone that it will have third party support and we had third party CEOs come on stage including EA to tell us that they will support it.
But once it came out, EA didn't even bother as well as most of them. The wiiU got terrible ports with missing content and performance issues with some games being delayed from third parties. And I think Nintendo was unprepared for it.
Now, while I agree that software output is one of their biggest issues and shared library would fix it, I don't like it due to the potential side effects. And they are essentially, why would I as a consumer buy both of their devices if they have the exact same games when I can just buy their handheld and a ps4?
Most gamers like Nintendo's handheld looking at their sales but Nintendo's consoles due to their power and lack of third party games such as cod, gta and etc don't really care for them. So I think the end result would have been similar with a shared library. Great handheld sales due to zero direct competition and poor console sales due to a competitive market and being able to play the same games on the handheld.
The console would have just been the gimmick where if I wanted to play on the TV or get a bit higher graphics, I would buy it but I highly doubt most people would care... Because they can just save that money and buy a ps4/x1.
Edit: Imo, their biggest issue was not getting third parties on their side for their console.
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