There's a nice extension that solves this problem called "clear-downloads", I like this extension because it only auto clears the download bar/ download history and nothing else such as cookies etc (I use other plugins for those already).
The extension auto clears the download bar/ download history of completed downloads every 10 seconds, which sounds heavy hitting to me, but so far in my experience I've not seen a decrease in web browser performance. What's more, source code is hosted on github.
Keep in mind this extension has no settings, and will not show up in the extensions bar (you can still get to it via the 3 horizontal bars > tools > extensions, clear-downloads) you will be expected to know where you saved your files. Loving this little niche extension though, it's gotten rid of the most annoying thing about Chrome for me.
clear-downloads via Chrome Web Store and GitHub