The built-in WebAssembly GC could just be the native JS GC, which is very, very good for most dynamic languages. There's really not that much difference between GCing JS, Lua, Python, and MyDynamicLanguageWithRubySyntaxAndLuaSemanticsAndNewFeatureX. I don't see why they'd need to do anything other than just expose the GC that's already there. Browser makers are smart enough to know "invent new GC that solves every conceivable language's memory problems" isn't going to work.

Since WebAsm is still Functional languages would still have the freedom to implement their own more efficient GC (avoid the write barrier in a lot of cases, scan only the young heap most of the time, etc).