In my limited experience, most browsers do what you describe already. Unless you type a 100% correct URL (and sometimes even if you do), a normal browser will send your URL string to Google (or similar entity), who will send back a redirect. The process is fast enought for you not to notice.

It is often possible (if hard) to configure browsers to do traditional URL resolving, but I wouldn’t bet on it always being possible. Google certainly has every reason to disallow reconfiguring their own browser to not send data to Google.