EDIT: Since no one seems to be reading the OP, I'll try to summarize some major points

1. The tablet is gone as Nintendo would have had no idea that it could take off, instead the Wiimote is the primary controller. That's $100 off the price right there, if not more.

2. The GPU obviously wouldn't be as great. It would be downgraded to match the PS3/360 in terms of pure graphical output.

3. The RAM would be cut in half, saving another $20-$30, and it would still be double what Sony and Microsoft offered.

4. A $50 loss is negligible in the video game business where most sales come from software, not hardware. Sony took a much bigger loss and still managed to succeed in the long run. 

So, a major problem that third party developers and consumers eventually had with the Wii and are currently having with the Wii U is their lack of power compared to the competition. This has me thinking, what if instead of releasing the Wii (which was a slightly upgraded Gamecube with motion controls), Nintendo released a traditional console about equivalent to the Wii U? Obviously they probably wouldn't have a gamepad controller, but using the wiimote as a primary controller would have still been innovative. 

The Wii U is based on PowerPC architecture, which would have fit perfectly alongside the Xbox 360, and the CPU is comparable in terms of power to the PS3 and 360. Now, the GPU and RAM that the Wii U has today would have been too costly, but 512mb-1gb of RAM wouldn't be impossible and a slightly downgraded GPU that could do DX11 would easily suffice.

All together, the hardware in 2006 would have probably be sellable at $400 if Nintendo was prepared to take a $50-100 loss for each system sold, which would still have undercut the PS3 and matched up with the Xbox 360. Nintendo wouldn't have pushed out nearly as many units, but it could have easily reached 60-70 million with third party support, and probably wouldn't be in the same position today, as the successor would probably be much more powerful (comparable to the PS4 and Xbox One) and would almost certainly have much better third party support.

Now, I'm not saying the Wii U isn't next-gen, it is and I love mine. It just feels like if they had released a slightly downgraded one in place of the Wii, Nintendo would be much better off in the long term, even if they lost those Wii sales.

They wouldn't have nearly the amount of money they have now. Nintendo wasn't at a place where they could sell a console at a loss like that.

A $50 loss isn't a huge deal, Nintendo would almost certainly make that up near instantly with their huge selection of first-party games that people would certainly buy when purchasing the console. 2 games and they've made a profit.

Also, they were bringing in a ton of money from DS sales. 

I actually think it would have sold really well! One of the main reasons why people aren't buying a wiiU is cause they already have a tablet that can do more... ipads/Galaxy tab and etc all are multi-touch, have a superior app store that are full of free stuff, and are also very powerful as well as being portable and not to mention most of the smart phones can do the same but back then when the wii launched, most of these things were just being explored. The first iphone came out in 2007 and it was terrible, it was unique but it was terrible so the wiiU could have competed back then as a viable platform as well as something "new" and innovative

But of course, the price could no way be $300, not even $350, the hardware probably costed a lot more back then and the tablet prices would also be crazy high so maybe not

If you look at the content avaialable and the market focus the Wii U is technically more the GC's successor than the Wii. Commercially speaking, the GC wasnt sure of its market visually nor in terms of content, but provided some hidden classics that not many people were able to try.

It would have been $399 at launch at least, and the casuals would have mostly ignored it, because too expensive. $250 made it so accessible to people who never bought a console before, and probably won't buy on again.

The real question is if Nintendo had produced Wii U so that it could have launched at $250 what would have happened?

It may have hurt Nintendo in the short run because the casuals wouldn't flock to it, but they wouldn't be in such a dire position as a console manufacturer if they still had the support of the core gamers and the third party developers. Nursing homes and waiting lobbies were never the most trustworthy consumers, but that's what Nintendo ended up targeting when it went full casual.

They sold 100m+ Wiis, all for profit. They wouldn't have sold nearly as many Wii U's, and would have made less money per sale. Nothing would be made up.

It would have been a HUGE success still. At that time tablets were still pretty new, people were going crazy over them, and it probably would have sold about the same as the wii. But the Wii U was too late to the party.

And now Nintendo is hemmhoraging money, and it will be an uphill battle for them to regain the trust of core gamers and developers. They may have made a nice chunk of money with the Wii, but now that is bleeding away from them and they may never be able to recover. 

I think that sacrificing a little short term profit in order to succeed long term would have been preferable.