That's true, if the Interface Types proposal gets accepted that overhead should be significantly less. At that point it'll get really interesting what the potential performance looks like for DOM-interaction heavy apps.
https://github.com/WebAssembly/interface-types/blob/master/p...
I wouldn't think it's far behind. The Multi-Value proposal, which had huge ramifications, was recently accepted in April so WASM is clipping along at a fair pace still.
Firefox Nightly and Chrome Canary both recently landed multi-value and reference types: https://webassembly.org/roadmap/
My understanding is that this is going to get a lot better in the future though -- last I checked the plan was for WASM to eventually have direct bindings to DOM APIs, at which point you won't need to interact with JS at all.