Apparently they aren't cool anymore so we need to spend another few thousand man years building another system in their image
They also, as you note in another comment, do not have the appropriate security model for web apps.
.NET 1.x introduced Managed C++.
.NET 2.0 replaced Managed C++ with C++/CLI due to feedback from C++ devs, regarding keywords and how GC types were declared. C++/CLI was submitted to ANSI C++ as standard proposal.
UWP introduced C++/CX, although it does compile to native code and interoperates with .NET Native instead.
Or Flash for that matter, which had a C++ compiler called FlasCC.
C++/CX is closer, but a) also still not the same language and b) doesn't run on the CLR, so isn't an argument for replacing wasm with IL.
WASM is assembly level just sandboxed and portable - direct memory access and basic instructions - it doesn't even have GC right now.
They are only superficially similar.
Providing a lower-level platform; directly exposing open web APIs. The first may not seem like an advantage, but it means more flexibility in the higher level systems (including runtimes like JVM or CLR, if you wanted to) that can be usefully run on top of it.