...in WASM you also call a function to do IO though? That function is just provided by the host environment via the function import table, but conceptually it's the exact same thing as a Linux syscall, a BIOS int-call or calling into a Windows system DLL.
As long as that function doesn't receive any parameter that is like any data actually on the DOM.
So you either create a very concrete JS library that translates specific WASM data into IO actions, or one that serializes and deserialize everything all around but can be standardized.
At this point, none of those options are much more capable than Java applets... Or, in fact, if you put a network call between the WASM and the JS, you won't even add much complexity.