You aren't competing with the site on Page 23, your competing with the sites on page ONE. When you are doing keyword research and find a well searched niche, you need to see whats on page ONE--thats it. Don't worry about how many sites show up in quotes or how many exist with the allintitle search.
I assure you that if you could find a keyword with less than 200 results in quotes and everybody on page one is optimizing for that keyword in a strong manner you simply are NOT going to rank very quickly.
So type in the keyword into Google with nothing fancy. No quotes, no allintitles, allinurls, etc. You are competing with those that rank for the keyword as its typed into the Big G and nothing else.