Wrong use-case. Animated GIFs and animated PNGs were never intended for video. The analogy to still image formats is video:JPEG = web-animation:PNG. You don't save screenshots as JPGs and you don't save photos as PNGs. Same with video and web-animation, two different use-cases require two different formats.

except that's a false dichotomy

one format can support both lossy and lossless images and use better compression between frames to achieve 10x better results for animations than animated pngs without visible loss of quality

Which format can support both lossy and lossless images?

I spent 2 seconds in GIMP to make the following GIF: http://i.cubeupload.com/kbrcfQ.gif Please show me the video format that can replace it.

webp supports animations, lossless and lossy images, etc. I already linked to a video with an alpha channel that can match your gif

When you can only post/upload content that end up inside img tag, it's not a false dichotomy.