If I'm right, we won't see wasm overused such that the web becomes a sea of monolithic and opaque apps (as too many mobile OS homescreens are). Per the FAQ, wasm is also for hot kernel code and reusable libraries helping mostly-JS apps.
It's up to web devs to keep innovating ahead of browsers, to keep pushing for better HTML, CSS, JS, and beyond. One way to do this might be via wasm modules that extend the web. The https://extensiblewebmanifesto.org/ project continues.