because the flow rate has to be controlled sufficiently so that you can tune it to be low O2 so NO3 gets respired away, (if I'm remembering right).
It'd be hard to control the flow rate with simply a bag of media.
The chamber serves as an anaerobic environment for the anaerobic bacteria to grow. As they are a key part in why this process works. That’s the short answer.
Try it out. Maybe a big enough bag, deep inside the media, will eventually become anaerobic and colonize some bacteria. However, having used a sulfur reactor and understanding the process, imo, it will not work.
One issue is that some bacteria may aerobically grow on the sulfur, converting it to sulfate and lowering alkalinity and O2. I’m not sure how fast that happens, however.