I have higher hopes for the web people (like PlayCanvas, Babylon, threejs, etc...) writing a proper WASM game engine by "scaling up" their experience of building browser rendering engines, than the traditional "native game engine" people "scaling down" to web requirements (especially when it comes to time needed to start into the game - the entire asset loading system of native engines needs to be rebuilt from scratch for this).
In regards to downloading assets, we've built out an asset streaming system to address this. It allows you to dynamically load in just what you need, when you need it, while everything else that isn't needed right away can be fetched at runtime.
And your assumption is based on what exactly?
WASM + WebGPU don't magically make the whole game, its assets and the engine it uses appear on your computer.