Try clicking one of the examples in the menu on the top, and then hit 'Play'.
Love it! It is certainly great for playing around with WebGL, but still lots of work necessary if it wants to catch up to Unity or CopperCube and create complex WebGL games or scenes.
That's mostly because of the architecture of Unity3D being both efficient and productive and UE4 being much more so. They're radically different architectures than what three/babylon have. And the fact that they both compile through Emscripten is proof AAA engines can be built for the web.
We're not too far away from SIMD, Atomics and SharedArrayBuffer as well as OffscreenCanvas in the browser (they're all available behind experimental flags today). I can definitely see a newcomer building a web engine from the ground up and beating Unity/UE4 in performance AND productivity for not having their overhead. Its a huge undertaking but nothing impossible.
What I missed the most doing WebGL work however were asset pipelines. Open-source engines barely support DXT compression, normalized integers and whatnot. We ended up writing our own (very crude) CLI tool to compress DXT1/5, ETC1 and PVRTC as well as a KTX parser to load them at runtime. I'll see if I can make them open-source - they're still a bit tied to our custom in-house webgl renderer.
We went with ImageMagick and PVRTexToolCLI driven from a node.js script. I'd go with GraphicsMagick now that I know about it; IM doesn't yield good DXT compression quality.
You are right with the lack of open source state of the art engines, it is a shame.
But you are misinformed about the webgl part: There are other Web 3D engines. For example Babylon or CopperLicht. The latter even has a pretty solid WYSIWYG 3D editor: http://www.ambiera.com/coppercube/
