It won't ever replace anything, because most folks don't understand the tech. I've no other way to explain this except to present this question: which is more popular, ASM, or literally any other higher level language (C, C++, etc.)?
Compilers, languages, and frameworks were built for ease of use for the end developer specifically so that any type of ASM would be avoided. Web technologies/frameworks along with Operating system APIs, etc. were a FURTHER level of abstraction. WASM has it's place, just the same as ASM has it's place. Trying to replace React with x86 ASM sounds foolish, does it not? The same goes for WASM. Why?
WASM is designed for situations where performant, low latency compute is needed, along with low level control, etc. Even IF they integrated DOM, very few would use it. Most of today's developers don't even know ASM for any platform, and they aren't about to learn it. They want to be productive, not rewrite basic stuff.
I mean shoot, as much as I dislike the AI bubble (AI/LLMs are great, corporate america is the issue), it is SHOWING what people want, which most of us already knew people wanted: we want to automate out the boring stuff and focus on the hard stuff.
> WASM is designed for situations where performant, low latency compute is needed
I don't get this argument at all. When is performance not needed? Every website can benefit from be faster than it currently is.