I think you are missing the fact that the only reason why your brick texture looks correct with classic mapping and not with the triplanar, is because your box's mapping is already stretched and when you combine it with also stretched texture, those effects happen to cancel each other in this specific instance. But if you'd apply the same texture to the box that is twice as tall as it is wide, you'd see that now classic mapping is stretching the texture even more than triplanar and you'd need to address this by adjusting either mapping of the box, or tiling of the texture (ideally you want to do both).
I'm not arguing against your request, actually i support it - option to "squarify" a texture with a single mouse click would be nice thing to have, it's just this has nothing to do with triplanar, like you're trying to show in the video.