I've done it for Virgil. It's a major pain, because Wasm, by design, does not give access to the value stack. So to find roots you need to spill them into memory into what is called a "shadow stack".
The problem with bringing your own GC isn't just that, though. It's that using linear memory for everything, you're forced to put external references in a table, which roots them. Tables aren't weak...and even if they were, it's possible to set up a cycle between the linear-memory GC references and external references so that leaks happen. This was a problem in other contexts, for example, in V8 embedded into Chromium, and the ultimate result is that you need cooperative garbage collection across two heaps, with queues. While V8 and Chromium trust each other, both not to screw up, and to be fast, it's hard to see how to make that cooperative garbage collection contract work with untrusted Wasm code.
The problem with bringing your own GC isn't just that, though. It's that using linear memory for everything, you're forced to put external references in a table, which roots them. Tables aren't weak...and even if they were, it's possible to set up a cycle between the linear-memory GC references and external references so that leaks happen. This was a problem in other contexts, for example, in V8 embedded into Chromium, and the ultimate result is that you need cooperative garbage collection across two heaps, with queues. While V8 and Chromium trust each other, both not to screw up, and to be fast, it's hard to see how to make that cooperative garbage collection contract work with untrusted Wasm code.