We don't have the resources to support transcoding, and since so much of our userbase is on browsers that support it I don't think we would regardless.
Not sure how you're going to solve the WebM hosting issues, but I would be really curious to see a list of issues large sites like 4chan have. I think me and other people would surely like to solve such «sysadmin/developer puzzles» for fun.
WebP is larger than APNG [1] and is supported more widely according to the following table [2]. There is a way to add compatibility to older browser too [3].
Other than that, there are also Opera [4] and Chrome [5] extensions for APNG.
Update: Found a successful APNG kickstarter campaign, which lists some interesting APNG tools and libraries. [6]
Also just tested myself how the filesize compares for different file formats able to host animated content for this source image [7].
WebP/M and H.264 are lossy formats, so any comparison citing one ultimate filesize for them is nonsensical.
I'd expect them to beat PNG with acceptable quality, since PNG's compression (gzip with some prefilters to make image data more gzippable) is the work of someone either limited by patents or not informed enough to make their own entropy coder.
Also try 'ffv1' in ffmpeg; it's lossless and will win every time.
Transcode a bunch of different-looking PNGs to a WebP losslessly, each pixel preserved exactly, and you'll see a byte savings in the neighborhood of 30%. Go lossy and much more savings, with the option of alpha transparency on lossy if you're into that.
It's not just efficiency, it's versatility that these formats bring to the table. Though the efficiency is compelling.