Not even law professors - typically, law professors have their JD (obviously) and then their Masters of Law (LLM), which is a post JD degree, specializing in a focused area of law (torts, intellectual property, etc.). Law school professors are typically referred to as "professor", or other academic designation - but to my knowledge and experience, never "doctor". While the J.D. is literally Juris Doctoral, it doesn't carry with it the title "Doctor" - we get other, special titles, "attorney, lawyer, esquire".
It's definitely a weird amalgamation of words and titles mixed in with history, but honestly, what else would you expect from the legal profession. We carved out our special snowflake designation centuries ago.
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The United States' degree of JD is not a baccalaureate level degree. It is a very difficult three year graduate degree, higher in equivalency than even a Masters Degree (which is typically a 1-2 year degree).
The JD degree in the United States is Juris Doctoral. In other countries, however, the law degree is a bachelor's level degree, like history or other such subjects.
The United States stole the British system of law (except for Louisiana, which uses the French version of law), and then morphed it into the shitstorm it currently resides.