I looked at the sample webp lossless images provided by Google.
Let’s see how do they look after we strip the transparency…
Notice the oddities on 1 and 4? This is a dirty transparency optimization. You can see the basic scheme explained here. This version looks to be the most advanced one, blacking out is good, but adds some edges that are uneasy for the codec to predict. Here, instead of black there’s exactly the thing that the codec would predict.
Certainly not PNG.
I tried CryoPNG on the image, which tries to manipulate dirty transparency so it works best with PNG. The best result looked like this:
Compression improved from 118.5 to 108.4 KB. The result can be seen below.
I suspected that Google chose the transparency pattern to make webp look good, so I tried to compress the image optimized for PNG with webpll, expecting to see the size increasing. Surprise, it dropped too. From 88.1 to 82.2 KB. So I don’t have an explanation for the pattern.