Not necessarily. GC can be implemented in a way that's fairly compatible with low-level programming, by leveraging support for multiple address spaces and/or memory segmentation. And WASM needs that kind of support anyway for its planned module-based security.

FWIW, AssemblyScript[0] adds its own garbage collection runtime into Wasm. The team had a good post recently on the performance implications[1]

[0] https://www.assemblyscript.org/

[1] https://surma.dev/things/js-to-asc/index.html

Not sure I understand. If parts of the runtime are already in the browser, then there's less to download.