So I'll drop this here, and take all the crow I deserve, when the times comes, admit I'm wrong and everything.
I'm not arguing this to be a jerk or delusional, and I can see Nintendo is saying the fan in the dock aids in the cooling. I agree like you quoted it does likely help remove heat. Logically it cannot remove heat from inside the Switch 2, when there's no holes for the air to pass through to get inside the Switch 2. But it can help cool down the outside, where it will be blowing air on.
But none of that is going to stop me from trying to achieve using the Switch 2 in a dock that is more portable than the one the system comes with. I did it with the Switch 1, and it allows me to connect it to XR glasses, and output to a 1080p, 120hz OLED screen on the go. Maybe it won't work. But, everything I've seen so far hasn't convinced me of that, and no one has made an argument beyond "Nintendo says so." - and even then they don't explicitly say anywhere it is incompatible with third party docks - because that would be pretty dumb IMO.
But we will see! If I end up losing a Switch 2 to satisfy my curiosity, that's on me, and I'll only have myself to blame. But I have had dozens of devices, handhelds, laptops, tablets, and plenty more powerful than the Switch 2, and they all work with docks without fans in the dock.
And when your dock is a mere USB-C cable, no plastic enclosure at all, there's no additional heat being built up around the Switch 2 in the first place.