Not to shit on my own profession (about this--there are plenty of other reasons for that), but lawyer education is nowhere near doctor education.

To paraphrase one of my professors, "Ever wonder why in the legal profession you can get a terminal degree after only three years without having to write a dissertation?" [Answer: It's because lawyers control their own profession, along with the government that controls how professions are regulated.]

On the OP, I don't think police should be required to pass the bar exam. The reason is that the bar exam, and by extension law school, covers much more material than police should ever realistically need to know, even being generous. Cops don't need to know which agents owe their principals fiduciary duties, for example. They don't need to be able to articulate contract remedies or determine when a party might have a prevailing argument against personal jurisdiction.

They should, however, have to pass a version of the UBE that covers criminal law and procedure in their jurisdiction, and they should have continuing education requirements. [And in many if not most or all US jurisdictions, they already do. --they do in mine, at least.] More importantly, they need to carry a bond.

In order for any of this to matter, however, first a court has to hold that the police owe a duty not only to the public at large but also directly to those in immediate need. In the US, the state of the law with respect to police and other state actors vis-a-vis victims of the torts and crimes of others is reprehensible. Take a look at Town of Castle Rock v. Gonzales, 545 U.S. 748 (2005), DeShaney v. Winnebago County, 489 U.S. 189 (1989) ("Poor Joshua!"), and Warren v. District of Columbia, 444 A.2d. 1 (D.C. Ct. of Ap. 1981). And if you like podcasts, Radiolab has covered this.

In short, the police need to be bound by a legal duty to rescue, and members of the public need a private right of action against agencies (police and others, including agencies like DCS) to whom private remedies have been surrendered when those agencies fail to perform their duties as required. It would require an upending of the American "system" in favor of something closer to civil law jurisprudence (e.g., the European continent). And it's desperately needed and long overdue.