How to make the Downloads-icon in Safari disappear?

I detest the Downloads-icon in Safari. So I always remove it by dragging it out from the toolbar when setting up a new Mac. Whenever I download file from Safari, I have a script that activates Yoink and puts the file inside it. So I don’t need the Downloads-icon in Safari.

But I still have to dismiss it manually in Safari, while what I really want is for it just to disappear automatically as soon as the download has completed.

Anyone have any thoughts?