A catch-22 in the Facebook friend process

Many people use Facebook only to maintain relationships with people they already know well, but one of the alleged benefits of the system is that it can also be used to make new friendships. Unfortunately there is a subtle but important catch-22 in the Facebook friending process which makes it impossible to decide whether or not I should accept friendship requests from people I don't already know.

Most people have set the security settings on their Facebook profile such that virtually nothing is visible to people who are not already recorded as their friends. As a result when I receive a friendship request from someone I don't already know I have no information on which to judge whether or not this is a person I would like to be friends with. Presumably the person in question doesn't mind me seeing their profile because if I accept their offer of friendship they will be revealed to me, so why doesn't Facebook reveal it to me as soon as the friendship offer is made? I know it would be possible for me to accept the offer of friendship and then reject it immediately afterwards if I didn't like what I read in their profile, but since it is considered very rude to unfriend people I normally play it safe and simply ignore such friendship requests.