Yes it does have to be downclocked. At full clock it would kill the battery of an iPad Pro (12-inch model) in just over 2 hours, and I'm not even accounting for the electricity the screen needs (since Shield TV doesn't have one). That would likely be another 1-1.5 watts needed per hour, so you're actually talking about battery life there in the range of 1 hour 50 minutes or something.
That's not even remotely feasible as a portable device.
And no there isn't a mobile chip available that runs way better today than an X1 without large scale throttling at max performance.
The chip you want is like a 10nm Tegra Next-Gen, but that's not coming until next year, and probably late next year at that.
1) Shield TV is not representative of the Tegra in the Switch. - Have you heard of a thing called binning? No?
If you are basing the 20w~ Tegra power consumption that is recorded from Anandtech here:
Do you fully understand the implications of recording power consumption from the wall?
Happy to educate you on the topic and how it also means the Shield TV actually uses less than 20w of power.
2) Again you use another device as some kind of representation of the Switch.
The iPad Pro has a faster CPU (Uses more power), larger screen (Uses more power), higher resolution screen (Uses more power), more powerful backlight due to the higher resolution screen (Uses more power.) and has various modems and logic in it's large SoC. (Uses more power.)
Now what part of the iPad Pro using more power are you unable to understand and comprehend? It is not an Apples to Apples (Pun intended) comparison.
3) Yes there are mobile chips that even whilst throttled are still faster than Tegra, maybe if you didn't base your opinion on Gflops as some kind of basis of determining performance, you might be able to understand that a little better.
4) No. I am not talking about "Next Gen Tegra". - Next Gen Tegra won't be 10nm either.
The next gen Tegra is the Tegra Xaviar, based on Volta, doubles the performance of Tegra P1 (Pascal) for the same amount of power and at the same node (16nm Finfet.)
I.E. Vastly superior to the Switch. And "Close enough" to the Xbox One in many aspects.
I don't think you fully comprehend how much of an improvement 16nm/14nm Finfet brings over 20nm planar process in terms of power characteristics.
It may use less power from the wall but it's not as if magically a 20 watt SoC is going to become a 8 watt SoC.
There's a reason why most tablet makers don't use a Tegra X1 and Nvidia was having problems finding vendors for the chip ... it's too beastly of a chip and consumes way too much power. That makes it better suited for the tasks of being a game machine than a tablet.
Running the Unreal Engine 4 demo, Nvidia themselves said the GPU alone consumes 10 watts of electricity. Then you have to factor in the RAM, CPU, WiFi, LCD screen, active fan, etc. all needing power too.
You're probably well past 15 watts ... 15 watts is a ridiculous power consumption for a mobile device.
Nvidia is also somewhat loose in how they define power consumption, they admit for example that even the older Tegra K1 can spike to over 10 watts of consumption itself when pushed to its higher peaks. Don't believe all the hype on power consumption with these chips, if they were really getting like 50 GFLOPS per watt, Sony and MS would be using them for their consoles too as that performance is way better the console GPUs they're using. My guess is in reality peak performance and electrical usage is not close to the ideal scenarios companies like Nvidia and PowerVR like to tout.
They know they can get away with it because most people only use their tablet for low level gaming and web browsing ... Switch does not have that luxury, it needs to be able to process relatively high end 3D graphics and that's where performance comes crashing down to the reality of what's possible with a 6000 MaH battery.
Even if you could put a ridiculous sized 12,000 MaH battery and made this thing a giant device, there are overheating concerns too, this thing has to be held by little 8-year-olds, it can't be pushing itself to the peak and getting hot to the touch. This is also likely why Nintendo does not allow the system to be held in docked mode, really if they wanted just TV streaming a cheap device ala the Google Chromecast type thing would've worked fine. They don't want kids holding the device when its running full tilt because it gets hot IMO.