However, for me personally I wonder: what's the point? I would go from Linux -> glibc -> native application to Linux -> glibc -> Web Browser -> WebAssembly application. Yet another layer of abstraction.
Sure, WebAssembly can be run directly on any platform. But precompiling an application is not a problem (my Linux distribution provides binary builds). So, this seems to be interesting to (primarily) web applications. However, I try to avoid web apps, because they are typically proprietary, a moving target, the owner can randomly decide to charge me for things, or (ab)use my data, and they feel non-native.
(I do see the benefit for people who use web apps, since WebAssembly is typically faster than Javascript and opens up web app programming to more languages.)