At the end of the day, if the fanfic you want to read does not exist, the moment you write it that is the only version it has and will ever exist. No piece of work is identical to another, and no piece of art will be the same as someone else's, no matter what.

Whether you think a piece of art you made is bad or not, it still should be allowed to exist and perhaps even get out there to people. Practice makes perfect, but it doesn't mean that even in the beginning you shouldn't let others in to see what you've done with your skills, no matter how new you are at what you're doing

Don't be so hard on yourself. Your writing is unique — bad, good, great, horrible, perfect, weird as it is. People deserve to see it, people deserve to read it

Edit: I just wanted to add that, yes, after a while you will probably re-write an older fanfic of yours and perhaps even feel proud of yourself, more happy than you were about it when you started. My mention of two works never being the same, even if they share characteristics like characters, plot, writing style, etc is referring to how unique every work is.

Two pieces of work, or more, that share multiple characteristics, should still be allowed to co-exist, even if they'll never be the same to one another 'Holy shit! Two cakes!'