It came out right when it needed to. Nintendo's timing is always perfect.

Hard to say.

Lots of factors are factored in when it comes to developers making games for a platform such as:

1) Platform holders working relationship with the publisher/developer.
2) Hardware. - More alien it is, the more difficult/costly it becomes.
3) Install base. - No point porting if they only sold 10 million hardware units in 5 years.
4) Time. - Publishers/Developers often have multiple projects being worked on, it takes time to port.

Hardware capability itself wouldn't have been a hindrance though.

Handhelds until the Switch usually always got exclusive spin-offs because mobile was simply a different experience, different form factor, different inputs. (I.E. Touch.)

In regards to specifically Breath of the Wild, it did run on the WiiU so it could work with 1GB of Ram.
Thus a handheld running with 1-2GB LPDDR3 1600mhz memory, 1.4Ghz 4x Cortex A9 cores found inside Tegra 3 would have been fine, it would have needed some visual downgrades though to actually make it work on the GPU side.
I don't think people realize how impressive Breath of the Wild is on low-end hardware, Nintendo did some incredibly engineering to get everything packed into that game and running the way they did with it's impressive physics and simulation.

Odyssey was built with the Switch hardware in mind, so it's requirements are arguably more demanding.

The Switch handheld itself isn't changing though.
You are just plugging it into a dock.

Which phones, tablets and handhelds have done long before the Switch even existed.

My phone isn't a hybrid because I plug it into a dock and it outputs to my monitor, it's still a portable first and purely a phone.

Nintendo needed to "differentiate" itself with a useful novelty, so throwing around buzz-words for people to latch onto like "Hybrid" is a good marketing tactic, it's a damn awesome handheld.

It would be interesting to see what a 2011 Switch's equivalent would be to the real Switch's Skyrim, Doom 2016, Witcher 3, etc, those really iconic ports.

COD would seem likely as Wii/Wii U got ports of Modern Warfare 3, Black Ops II, and Ghosts in 2011-2013.

Would a downscaled port of Skyrim be possible on a Tegra 3, or would that be a bridge too far?

I've got some pretty low-level understanding of Net Immerse/Gamebryo/Creation engines as I was part of a group who reverse engineered the shaders in Oblivion and Fallout 3 to run on Original Xbox equivalent PC hardware back in the day. (Shader Model 1.0 on Geforce 3 Ti+Pentium 3+128MB Ram.)

Skyrim specifically can scale downwards to stupidly low hardware levels, it would still handle the same game world, but textures, lighting and shadowing would end up being around Morrowind equivalent levels, with longer draw distances.

It helps it was on the Xbox 360 and Playstation 3.

Call of Duty would be fine, they might be 30fps ports with a few concessions though.

Hm, I don't know, wasn't Vita compared to Tegra 3 back in the days (via iPad 2 vs Tegra 3 benchmarks, and then extrapolated) and came out fair bit on top?

Virtual Boy, N64, GameCube, and Wii U would beg to differ. 

But the unit does change when docked, does it not?  Docking allows increased clock speeds which improves performance and/or graphical fidelity, which is not possible in its standalone handheld form?

I don't think it would have made a huge difference.

There were certainly hardware flaws with the Wii U, but I think people underestimate how much of its failure was due to bad games.

For me, I was bullish on the Wii U. I thought the hardware design had potential. The moment I thought "oh wow this thing is doomed" was at their E3 conference where they showed off Mario Kart 8, Wind Waker, Tropical Freeze, and Mario 3D World. All of these were actually good games, but none of them were system sellers. They were pretty safe and mostly unambitious sequels. The same thing can be said for a lot of the Wii U's lineup. NSMBU, Game and Wario, Wii Fit U, Wii Sports Club... There just weren't a lot of great games for Wii U, particularly in its first year. They did get some games that could have moved hardware later on (Mario Maker, Splatoon, Smash 4, BOTW) but it was too little too late.

In this scenario, we basically have the 3DS but with remote play as the key selling point instead of the 3D feature. That's definitely a plus. I personally love the 3D, but I'm clearly in the minority on that one as most people think it's a minor addition at best. So, that would probably boost sales somewhat, but assuming they didn't have a massive price cut as they did with the 3DS in reality, that will be mitigated. Also, I don't think the play on the go feature is as appealing with 2011 tech. I feel like the gap between XBox and Xbox 360 was much bigger than the gap between PS3 and PS4 (in terms of the user experience, not necessarily the technology). The Switch I feel offers something that feels at least comparable to what was being offered at the time with the PS4/XBone. So, it feels at least close to playing console games on the go, whereas this hypothetical system would feel more like playing handheld games at home. That said, I still see that boosting sales of the 3DS by a decent amount. Like 10-20million just to throw a number out there.

Then, what does the Wii U lineup add to the equation? IMO not much. First off, they would be redundant. Early on the only noteworthy game would be NSMBU, which would be an upgrade over NSMB2. Then there wouldn't be anything really of note. They wouldn't do two Mario Kart games, so we'd just maybe get a better version of 7. 3D World and Land are also sort of redundant, but maybe they'd release World as a sequel. Either way, wouldn't do a whole lot. What else was there really that's going to push sales?

The TL:DR version of this post, is that I am firmly of the belief that the biggest problem with the Wii U was actual its incredibly mediocre library. Adding those games to the 3DS wouldn't have helped its sales all that much, particularly as the 3DS had similar titles. The Switchability feature may have helped modestly.

With regard to Tegra 3, what kind of performance gains could be attained by running it in a docked configuration with higher clocks due to not having to worry about battery life?

It physically doesn't change.

Having clockspeeds change when plugged into mains power is actually a characteristic of a mobile device.

Pretty much all phones, tablets, handhelds, laptops will run at higher clockrates when plugged into mains power or "unlock" a higher boost clock rate.

Really depends on what kind of cooling system is in place, and base clocks you have while mobile, thermals and battery life tend to be one of the biggest limitations.

But a 50% boost wouldn't be unheard of once you don't need to concern yourself with the battery or thermal performance.

Cortex A9 is good for around 1.5Ghz, I would expect while mobile 1Ghz or less would be the norm.