I think it would have probably gone worse than the actual WiiU. Reasoning: with the higher power it would have put even more strain on the dev-teams as it actually did, as the gamers expectations would rise with the possibilities and they would expect more polys and higher res textures. So development times would have been even longer. On the 3rd-party category I don't see much difference. Big AAA 3rd-parties would have mostly avoided the WiiU still, as multiplat games would still sell with a similar distribution. For small indies it would not make much difference, maybe the dev-kit would've been more expensive and so the hurdle higher. Overall I think the WiiU would've ended not with more but with even less games. Sales would be similar though, as most of it's sales were by trusty Nintendo fans anyways.

The system would sell at least Gamecube numbers, but the PS4 would still dominate it.

Without the gamepad, people would be far less confused as to what the system was and there wouldn't be that large contingent who thought it was just an add-on for the Wii. That alone would make things much better.

PS4-level power would ensure that 3rd parties support the system. If porting games that are already multiplatform is easy, then developers will have little reason not to do it. So even if Nintendo struggles with output at first, the console would likely avoid the dreaded drought of early 2013.

Abandoning the Wii's mass appeal strategy would badly hurt sales, and the 'core gamer' crowd would get the PS4 over Nintendo's offering no matter what. Most of Nintendo's sales would come from people jumping ship from Xbox.

The biggest question is how well Nintendo would be able to capitalize on the mistakes Microsoft made with the launch of the XB1 that handed Sony the generation before it even started. Depending on how Nintendo played their cards I could see the system selling as low as 25 million units and as high as 50 million, with the lower end being the more likely scenario.

A holiday 2013 launch with Super Mario 3d World but with early PS4-level graphics along with Wind Waker HD, a reworked Nintendoland, and Pikmin 3, together with 3rd-party games on-par with the PS4 versions would do great out of the gate but wouldn't have the same momentum the PS4 had. It wouldn't lose momentum the same way the actual Wii U did, or how the N64 did, but it would fall to a distant second very quickly under even the best possible circumstances. I doubt even Mario Kart 8 would be enough to have Nintendo keep pace with Sony for long. People just weren't going to abandon Sony even if PS4s were discovered to have a 50% of spontaneously combusting and burning their houses down.

Wouldnt say so.

The GameCube:

• released at a time where the PS2s integrated DVD player was a major USP
• once again screwed developers by using low capacity mini dvds
• is the successor of a (comparatively) "flopped" system
• released after the PS2

The WiiU

• released when a DVD/BlueRay player wasnt a USP anymore
• supported standard discs
• is the successor of a successful system
• released before the PS4

My conclusion:

The hypothetical "playstation WiiUs" life cycle would have probably played out similar to the XB360s

There would still be (still is) the perception that "Nintendo fans only buy Nintendo games" and Nintendo would still be trying (often not hard enough) to push that boulder up a hill. That was true in the GCN days and only became stronger in the Wii and Wii U days. The GamePad was a big turnoff for devs and gamers, but even if the primary controller was a standard Pro Controller, how does Nintendo get Madden/CoD/2K/Ass Creed/whatever big AAA gamers to uninvest from their current platforms where all of their friends and trophies are and game on the Wii U, with its inferior network and storage capacity?

That's what TeachMeHisty means by this hypothetical version of the Wii U being GCN all over again. We'd look back on it more fondly for its game library, but it would still miss out on a lot of big third party games or get half-ass ports, leading to a self-fulfilling prophecy.

The Switch is changing that perception because it's the Nintendo console that clearly gives an answer to why people would choose the Switch version over, or in addition to, another console version.

Also, let's not forget the Wii U was still on that played out as hell PowerPC architecture from the GameCube days. In this scenario, does it still have a PPC processor, or a more modern one?

If it's the latter, then does that mean no Wii backwards compatibility, or how would that be handled?

Yeah. The number of third-party games bigger than the miniDVDs 1.46 GB limit are exaggerated, but it nevertheless was a bottleneck. A lot of the demanding third-party games that didn't make it to GameCube would require compression, 2 discs, or would be virtually impossible. 

The N64's cartridges were a much bigger problem to devs, but N64 still sold more because it was coming off of the SNES and it had the triple-whammy of Super Mario 64, Mario Kart 64, & Ocarina of Time. 

25 GB wasn't too bad of a limit for Wii U discs, but Wii U would likely use Blu-rays in this what-if, allowing them to store up to 50 GB. However, it would have to have mandatory installs like Xbox One and PS4 so that the games can actually run. 

My dream come true lol. Since Wii, I have fantasized routinely about another Nintendo console that not only goes toe-to-toe with whatever Sony and Microsoft puts out, but one-ups them. Super powerful hardware, standard controller, standard media delivery etc. Could you imagine? All the Nintendo goodness with the hardware for GTA and any other game that developers create. It would be unstoppable... at least for me. I don't know how well it would actually do. It could flop. But hey, I'd be in heaven!

Would the software droughts and the 3DS still exist in this scenario? Because if so I don't think the Wii U would've done a lot better.

Unfortunately, the Wii to the present pretty much killed that. Nintendo is way too far behind to play catch up even if they released an enthusiast/Pro SKU alongside a normal one. 

Nintendo isn't going to release a hybrid around PS4-to-PS4 Pro level and then at the same time (or a few years later) release a home console Pro version that's around a PS6 or at least halfway between a PS5 and PS6. Nintendo's titles wouldn't take enough advantage of it, and even with optimization I don't see third parties seeing it as viable enough to release their games on when PC, PlayStation, and Xbox are easier.

We don't have full sales data for PS4 Pro and Xbox One X. If this figure is to be believed, PS4 Pro sold 14.3 million units by 19 January 2020. Going by the over 105 million PS4s as a whole sold to that point, that's more than 1 in 8. But it's lower than 1 in 7. Granted, the Pro didn't even release until November 2016. With Nintendo's desire to not lose money on hardware, I don't see them developing a very powerful SKU that would sell 10-15 million units out of a platform that would probably sell over 100 million total.

I agree

People saying it would sell less than Wii U confuses me 

If the system have the same capabilities as Xbox it would likely get the same third party support as Xbox, which means it would get the third party player crowd 

Many of the games and system sellers on Switch would end on Wii U instead

Would it sell nearly as close as Switch? Of course not, but it would sell much better than Wii U, probably close to XBOX One current sales