I had an idea about capturing games that I've never seen tried out and I'm wondering why.
I got some decent results capturing DS footage directly with my webcam many years ago, having my webcam propped up in weird ways to get it angled directly at the screen, of course it was a bit tricky to play like this and I couldn't hold the console completely still.
When fully in focus the camera would get some weird rainbow glare so I had it slightly out of focus which meant the image wasn't perfectly clean but it was still in focus enough that you could see individual pixels.
This made me think, wouldn't it be relatively easy to reconstruct the original image by using some simple form of image recognition to crop out just the screen (as long as everything stayed in frame at all times), given that the camera was high resolution enough and of good enough quality to discern individual pixels without excessive noise, and resize it to the correct resolution, applying some filtering to filter out the noise? The colors and contrast would always be off by at least a little compared to a direct capture (depending on the quality of your camera), but it would still be a huge improvement over just recording the screen with a camera. It would eliminate the shaking and for all intents and purposes should just look like a slightly desaturated direct feed, and you may even be able to fix that by filtering it and calibrating the filter so the colors look as close to original as possible.
It seems like it would be such a simple thing to make a generic program able to do this, especially with modern computers having enough power to do it in realtime with ease. The only tricky part would be calibrating the filter to look close to the original with your particular camera, as that part of it would vary by camera, but it's not strictly needed.
Of course it would be much easier to actually play the games if you didn't have to hold it in a specific way and prop up the camera but people who can't afford or aren't willing to spend the money on a capture card (or there just isn't one available for their preferred system) still do this anyway and it seems like it would be a godsend to those people.
First of all, this thread here is kinda outdated. HorizonMod has been re-written from the ground up and can get very good FPS with nice quality on N3DS systems with stable 60FPS on N2DS (because of the extra processing power over N3DS).
However, as far as other alternatives go, you can always open up the 3DS shell, find the ribbon cable that goes from the GPU to the screens, trace the pins in it to see what handles what (eg: colors, pixels, power, ground, etc.) and map those to the pins of an HDMI cable, then assuming you know enough about electronics to make your own circuits since you have gotten this far, just design a small converter board to convert the signal to HDMI and output to a TV, which can then be used with anything that can record (VCRs, console capture cards like the Elgato which are pretty cheap and so on), but know that you WILL lose all functionality from the screens AND it may eventually fail since HDMI signal output requires more power than what the 3DS is allowed by it's battery and PSU to go to the GPU. DVI-2 (the version with the flat pin without the two pins above and below the flat one) output is the only one that uses a level of power the 3DS can handle. Capture cards don't "steal" the signal, they copy it, reason they can bypass power limitations as they don't have to force the GPU to send out consistent max FPS signal that won't have losses upon conversion.
Another option would be to just design your own capture card, which takes slightly higher level of skill than the above method but lets you use HDMI. It's not anywhere near as hard as it sounds honestly, you just need a VERY good grasp of how the console works then an understand of video capture.
I did not know HzMod got such a large update, haven't seen that mentioned on the front page or anything. Still, the lower image quality mentioned in the OP is a valid point. JPEG (or other heavy lossy image compression) does not look great, and with the added compression of whatever streaming service if you decide to stream the games or even the added compression of a YouTube video, it will look doubly bad. It may be good enough for a stream that will only be shown once but for a video that will be viewed numerous times over however many years and will either give new visitors a good or a bad impression of your channel it could matter a lot more.
Couldn't the converter board just be externally powered, solving the HDMI power issue?
Also, about the n2DS thing, can't you use the extra core on a n3DS when 3D is turned off?