Writing is difficult work. To make a decent piece it not only takes a great deal of effort to create a draft, but there must be a rigorous editing process. All writers put some of themselves into what they write: their time, ideas, passion, etc. So, no matter how bad you might think it is at the time, don’t throw it out. Often it takes many iterations and an indeterminable amount of time to get it right.
Once you have written a piece, then you will prepare for another important step in writing, the editing and/or re-writing process. Do not throw out your work, whether it be the only draft or a beginning of a future draft. If you do, you might regret it later.
There are pieces of my writing that I have completely thrown out over the years. Why? Because I was never going to try and get them published. One of them I recall was when I was a teenager. I had written a piece and the characters had been linked to a television show, which means that even if I had wanted to publish it, I didn’t own some of the characters. However, these pieces are still a part of our writing history, and we may want to look back at them someday.
So, no matter how short of a piece that you have written, or how bad you might think it is, do not shred it or delete it. That bad story idea could be a future good idea someday. Sometimes, all it takes is a sentence to send your brain and writing into a completely new direction. That sentence might be part of something that you wrote a decade ago and felt was awful at the time. But inside there was a forgotten gem.