Google's link search behavior and a Firefox request

It's annoying to have so many text entry fields at the top of a browser. There's one for a URL (which may act as a search field), one for search (which may allow specification of the search engine) and one embedded in the Google or WL toolbar (the latter can be set to search Google.

It's no wonder users get confused:

Google Tries to Fix Broken Links

....So people type URLs in the search box. Google changed the way it treats those queries last year: instead of showing information about a URL, it returns standard search results and the top result should be the page that corresponds to your query. This is a great way to avoid typosquatting sites, like flicker.com or twiter.com.

But what happens when Google doesn't find a page from a site included in the index? Until recently, it returned the standard 'Your search did not match any documents.' Now it returns more helpful information: results from websites with similar addresses, suggestions for queries and a way to identify the page by restricting the search to the domain/subdomain from my initial query.

This is a great improvement that should be emulated. It's one more step in the "brute force" approach to broken links. We're stuck with "brute force" because the web never evolved a true directory service.

Now I'd like Google (or Firefox) to add an option such that when the URL matches a well ranked site then we just go to the site. We'd only see search results when the URL was off, that would be the current behavior.

This might have to be an advanced option since the variant behavior would be confusing, but it would let me live with a single top text field. One that also needs to mapped to command-L (OS X) or Ctrl-L (Win).