If you want to compare the situation to x86, direct DOM access for WebAssembly is more akin to the BIOS than C++ stdlib access. If it can't interact with the outside world, it's just a very special toy that you can only use to play a game that isn't any fun, and a good candidate for those 'What's the next COBOL?' discussions that come up every now and then.
It's basically that joke about Haskell, that nobody uses it because it can't have any effect... but for WASM the developers are insisting on making sure it's real.