This is a good point. The discarded stuff will doubtless also contain something that can be recycled, or simply serve as a negative indicator of where to go next.
I ended up writing a short story yesterday that I wasn't really convinced about. But I''d had the idea, and fel that I needed to get it done before moving on to anything else. It had been bugging me for a while, so I just wrote it down and released it, thereby releasing myself.
Publishing fiction on Medium doesn't quite count as 'tearing it up', but it's not far off sometimes!