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I think that for short-term encounters "rich" is a proxy for sanity. It means they have jobs that bring in good money; which means they need to be integrated to the society to some degree and wouldn't have too much time to be focused on stalking someone. It also means that they have something important to lose and have an active interest in not freaking a woman out.

"educated" could be a substitute for "rich" - and the educated, good looking, but not very rich people would be ideal for dating sites.