Batman is the world's greatest detective. His villains need to compete on an intellectual level, and in fiction a doctorate is short-hand for "smart" and "an expert in the field."
My favorite moment from the old Batman animated show was when the rogues were sitting around telling their stories about how they almost got Batman. Actually, I wouldn't do it justice, just watch it here:
He doesn't have a doctorate but Joker is stated to be an expert chemist almost on par with Scarecrow, just different focuses.
Ra's Al Ghul is 600 years old, a master of multiple martial arts and languages, has first-hand knowledge of all kinds of history, and is the leader of the League of Shadows.
And I'd be willing to throw most supernatural villains in the list too.
Tom Elliot was one of Bruce's childhood friends, but always kind of a psychopath. He set up his parents murder, and then used his inheritance to go to medical school and become a master surgeon.
Continue the thought to its natural conclusion: That was back before degrees were financed with tax payer money... which allowed people to fall into indentured servitude with debilitating repayment schemes that most will carry until they die. Pros: Someone way smarter than you is making your coffee, waiting on you, driving you around, and delivering your packages. Cons: Society doesn't actually get to benefit from the advanced degree it fronted the money for.