My 3DS opens that no problems. Even the full Twitter page no problem.Takes probably 1 minute (yes abit slow)I wouldn't mind a YouTube client for 3DS. The problem is, it will never happen.
Firstable, let's forget about running any videos in 3DS' browser. It can barely render web pages! Just try opening a regular (non-mobile) version of Facebook and wait until you die... and then wait again when you scroll a little bit.
Then, there's the problem with 3DS' hardware. Youtube sends videos either as MP4 (H.264) format, as WebM and as FLA (various proprietary Flash codecs). 3DS is definitely not powerful enough to decode H.264 nor WebM (which have similar complexity), especially that its GPU does not support programmable pixel shaders that would help to offload the work. And to get access to Flash proprietary codecs, Nintendo would need to pay Adobe.
Of course, apart from shitty 10-minute camera recording which waste enormous amounts of space due to a primitive MJPEG codec, 3DS is perfectly able to play high quality videos. After all, we can see them in eShop and in Nintendo Video. The problem is that Nintendo uses a proprietary paid codec ActImagine/Mobiclip, which will never be implemented by YouTube.
Adobe for mobile is also abolished.
But other than these, pretty much agreed with the rest. I can't say that the 3DS is so damn powderful or weak like shit because I have absolutely no idea of the specs, but a YouTube app just seems really really unlikely.