Earlier quoted context omitted.
To be fair, a generational mark-sweep GC algorithm doesn't take much more space over the compile-time modifications to the code itself. A reasonably performant GC algorithm suitable for most front-end work would probably only add about 10 kilobytes to 20 kilobytes of code to an executable. That can be downloaded and cached in the blink of an eye.
The problem is that you need to get all the GC root nodes on the stack. This is platform specific and must be implemented by the browser. The only crossplatform way is to create an additional shadow stack that contains only the root nodes but this means you pay an additional cost for the GC on every function invocation.
It can be done. There may be pain, but the pain can be managed.
EDIT: by that I mean that one would need to maintain two heaps. One for data that interacts with the browser and that is wrapped by the FFI as external resources, and one for the internal system itself, which can be managed via GC. Only the WebAssembly code would have to manage GC roots, which can be done as per any GC language.