You can hide the find bar with the ESC key (set focus with Ctrl+ F if necessary) if you do not need it and only display that bar if you need it or use Quick Find by pressing the / key.

I think you are missing the point entirely, or maybe I am not explaining it right. My find bar is in view 24/7. I like in view as I use it all the time. But it it ridiculous to have it take up a whole row. It doesn't make sense that you can't drag it to the Add-on bar. Look at images below.

I don't know of a way to position the find bar items on the Add-ons bar or place other items on the find bar.
That is why I wrote my above response to hide the find bar if you do not need it.