Of course you can build a GC in WebAssembly. You might have to avoid the native stack and lose some performance that way, but that shouldn’t be too bad I think.
One problem is that this GC doesn’t interact with the browser’s GC in any way. So you have painful memory management interactions when (for example) a DOM event handler references a WebAssembly object which in turn holds a reference to a browser object, possibly with cycles (so simple reference counting isn’t enough).
You can fall back to manual memory management here, but that’s painful to use. To make this work seamlessly, you need a way to trace references across both heaps in one swoop. Last I checked, there was standardization work underway to enable that.
One problem is that this GC doesn’t interact with the browser’s GC in any way. So you have painful memory management interactions when (for example) a DOM event handler references a WebAssembly object which in turn holds a reference to a browser object, possibly with cycles (so simple reference counting isn’t enough).
You can fall back to manual memory management here, but that’s painful to use. To make this work seamlessly, you need a way to trace references across both heaps in one swoop. Last I checked, there was standardization work underway to enable that.