Not nearly as well as the other way around I'd say. But I can say that Wii Sports did sell because of Wii's hardware, and userbase is an important factor to if dev will support a console with 3rd party support (though that doesn't really mean BETTER hardware will always win out and get the best support).

Your statement is only true in a very few circumstances.

Likewise, software selling hardware is only true in certain cases. But both statements are truth, regardless.

Most systems these days have good to great content though. 

It's not there's nothing to play on the XBox One, yet it's selling considerably less than the Playstation 4. 

So I'm not sure how true this adage is, besides Nintendo's problem isn't so much with not having a lack of Nintendo's own games, it's kinda everything else that's the issue. 

The days of systems like Atari Jaguar and 3DO having just objectively bad libraries for the most part are over though. Everyone has good games now. 

There are far more instances where consoles get a bump in sales when good software is released. It's WAYYYYYYYYY more common than hardware selling software.

No, no it doesnt.

Sega Genesis was superior hardware to NES.
N64 was superior hardware to PS1.
Gamecube was superior hardware to PS2.
PS360 was superior hardware to Wii, yet Wii died out when it clearly didn't get the 3rd party software. This actually shows how Wii was hugely successful due to early software, then died out long-term as other consoles software prevailed.

PS4 is the first time in the history of games that the superior hardware is also the sales leader. Again, it is due to atleast being on par software wise with everyone else, on par with price, and then differentiating on slight differences in hardware. (also brand popularity especially in EU)

Data demonstrates over and over again that software sells hardware.

It is kind of ridiculously one sided how many times software has shown to move hardware compared to hardware moving software. 

Literally all the consoles you've listed helped selling software. You didn't disprove my point, you just made clear powerful hardware doesn't necessarily have to move more software than less powerful harwdare.

Being the defacto leader for third party games results in high sales. 

But the NX is unlikely to have the best third party support. The GameCube probably had the best 1st year lineup software wise ... 

Super Smash Bros. Melee, Super Mario Sunshine, Metroid Prime, Animal Crossing, Luigi's Mansion, Pikmin, Wave Race: Blue Storm, Pikmin, Star Wars: Rogue Squadron II, Resident Evil REmake, Eternal Darkness, Resident Evil 0, Star Fox Adventures, Super Monkey Ball, all in the first 12 months of release, all exclusive (this IMO pretty easily beats even the Wii). 

Still had poor sales. 

Having a good first year lineup certainly doesn't hurt, but it isn't the be all, end all either, especially since unless Nintendo is releasing several hundred games in a year, the PS4 and XB1 will both have better libraries. 

They need to have a novelty/hook to the system or a diffeniator that people look at and overwhelmingly say they need that in their life (above and beyond just great Nintendo games). 

True, but that inherently isn't power. Software on the other hand definitely offers reason to buy the platform, and is proven to help the sales of hardware. 

So really, innovation and software are the two biggest things that will give the NX success, not power. 

NX just needs to be profitable at a reasonable level for Nintendo.

It doesn't need to sell 100 million units (for the console variant anyway).

Even 35 million ... I would consider at this point to be a fair success given how the Wii U finished and 40 million to be something Nintendo would be quite happy with. I think if you gaurunteed them right now 40 million in sales but no higher for the console NX, they would take that and run. 

They will make hundreds of millions of dollars every year from mobile, NX doesn't need to be the be-all, end-all, but even 35-40 million isn't a lock by any means. They need to work very hard to get to that.

Sony and MS have long headstarts too, that's problematic.