What's needed is a compression method that doesn't introduce artifacts on hard edges, as JPEG does, but is otherwise no worse at compression than JPEG. Then we wouldn't need to do some things in JPEG and others in PNG, and we'd be spared the pain of JPEG screenshots. Much better results on the Tecnick image set (which is mostly hard edges) would indicate one had been found. The results only indicate modest improvement in that area.
In particular, look around her face, eyes, and the background. The JPG is not just worse, but in fact very worse.
A more serious flaw is that it doesn't support animation. It doesn't need to be a video format. It just needs to be able to play a sequence of frames in succession. This is as easy as including a header that specifies how many frames are in the animation and the duration of each frame, followed by the image data itself. The fact that PNG doesn't have this has plagued the format since the internet became popular.
That may seem like "a video format," but it's not. Video decoders optimize for inter-frame compression, not intra-frame compression, so it's a different problem altogether. BPG doesn't need to do everything, but it should probably have basic animation.
That depends on what you mean by "worse" and "very". I think for most use-cases, those differences are not something likely to be noticed by the majority of users.
Again, JPG is not merely worse, but very worse. In fact, JPG makes it look like she's wearing a hat that's made of crosshatch material at the top, when in fact the top is composed of rings of fiber, not crosshatch.
What's needed is a compression method that doesn't introduce artifacts on hard edges, as JPEG does, but is otherwise no worse at compression than JPEG. Then we wouldn't need to do some things in JPEG and others in PNG, and we'd be spared the pain of JPEG screenshots. Much better results on the Tecnick image set (which is mostly hard edges) would indicate one had been found. The results only indicate modest improvement in that area.