Unlikely. There's a stigma against Nintendo in the West for some reason. 

In other words, parity is, regardless, not a winning factor for Nintendo.

But then, wouldn't parity change the attitude of certain companies like Epic, which demand certain HW specs to fit their own agendas?

If you are talking about support from 3rd parties, I think WiiU will have it, just thinking about the economy and all the money needed to make a game now-a-days, I'm pretty sure WiiU will not be Wii all over again... Now, it's pretty much impossible that one console gets 100% support from 3rd. Parties!

Perhaps it would if it happened several years ago, so before the Wii. But now there's an established fanbase and perception towards Nintendo and their systems which most developers cannot just overlook, even if the Wii U was more powerful than the other systems (see GameCube).

Only difference (and the intent of OP was to show that), is that the cube had parity but it didn't have the winning strategy (like Wii does).

I'm thinking of a case where the system has both the winning strategy and parity. Would 3rd parties bite, and what would that require? Loss-leading?

Also, would it cater to the mass market (wii strat) without the value-add (e.g. motion controls, padlet)?

It could happen, but not to the Wii U though!

Nintendo would never have mega sales and hardware parity. If Nintendo had the most powerful machine on the market, best multimedia functions, and best online, they would still only sell it mainly to the hardcore Nintendo crowd. Casuals wouldnt be interested, and the Sony/Microsoft crowd or so called hardcore games wouldnt budge either. They are programmed to hate Nintendo, and once a Nintendo hater always a Nintendo hater.

Until they grow out of their teens or early twenties.

I meant success in terms of SW sales and HW sales, not margins on HW.

this is going to sound messed up but, they need to not release hardware that sucks IMHO. They can make all the unique crap they want, but if its not up to 3RD party standards, not Ninty standards, some 3rd parties wont mess with them, its that simple. You cant make decisions like going with cartridges, even though everyone told you not to do that, and expect people to roll over. You cant make a purple GC that does nothing to differ itself from the comp and expect results,to be fair the GC did get alot of support no matter what some might think. YOu cant release a console that barely is stronger than your last one, when an HD console had already been on the market for a YEAR. you cant release another console that is barely stronger than consoles that have been on the market for SIX to SEVEN years. YOu cant do these things and expect to be treated like the other guys, becaue you are not the other guys.