Hi Broni.
The actual problem here is the fact that googling a name gives information (maybe too much information) about said person. But if you un-check the last one ("Create a public search listing..."), this information isn't transmitted through search engines. I like the other options because I can see who is asking to be my friend, or who I will be asking to be a friend.
The search in Facebook doesn't do any wrong. It's there for a good reason. If it weren't there, facebook's usefulness would end.
Two-Eyes