Totally agree that this should not be part of the browser address bar. That's specifically for one thing only: changing the view of the current browser window (either by searching or putting in a URL). It will start to get messy from at UX perspective if you try to mash the find in page mode with the address bar. For one, it means the user has to figure out what mode they're in after they've searched within the page - am I in find in page mode, or can I type a URL and have it work?
There are very good reasons for keeping the two of these as separated UI elements and user confusion is a big one. Happy to go into more detail if needed.