In the US the primary reason to go to law school is to receive the credentials and certification necessary to practice law (even if one actually doesn't want to be a lawyer, which turns out to be quite common). The legal profession is easily the most well represented (har har) profession in the entire country, and has extensive power to lobby on behalf of their own interests.
The primary bar that must be met by legal students is, well, the US bar exam, which requires a J.D. in about 45 states. The American Bar Association (ABA) is an extremely powerful professional/lobby group in the US, and in fact is so influential that a section of the ABA is actually responsible for the accreditation of J.D. granting institutions in the US. According to the ABA, "forty-six states limit eligibility for bar admission to graduates of ABA-approved schools". If the ABA wants to require students to play the Hokey Pokey at a World Championship level before studying law, they could very well make that happen.
Interestingly, the J.D. itself has a surprisingly short history, being formally instituted starting in 1962, and the "LLB" (bachelor of law) was considered sufficient to be a lawyer for still more years after that. Before that, one did not even need a college degree of any kind to be a lawyer, and lawyer was like nearly all other professions in that they did not require a college degree to enter into them.
Officially the reasons for this was a concern that the existing 2-4 year degree along with the apprenticeship model was producing many lawyers who weren't fit to serve their clients. Thus the goal was basically to "improve education", or simply to let less incompetent lawyers sully the name of the profession.
Another interpretation is that this was rent-seeking behavior, specifically in the form of economic protectionism of a profession putting up artificial barriers to entry to restrict the supply of labor and thus increase the prices that could be won by those on the inside of the system. Any benefit to clients would be secondary, in this interpretation. This time period saw the rise of using University education as required credentialing of many professions in the US.
You might also note that the sudden adoption of the increased credentialing of many professions happened right around the same time as immigration law in the US was changed and major increases in migration increased supply of foreign-educated and foreign-trained professionals in the US. A cynic might suggest that lawyers-as-politicians voted against a form of labor protectionism in one area, and then turned around and voted themselves unique labor protections to guard them from harm resulting from their other decisions. I would of course never suggest such an uncharitable view of our late, great statesmen. (cough)
I'll leave it to you to decide how to mix and match these interpretations of why things are as they are now.
By requiring additional education far beyond pretty well any other country, the US transformed in about 100-150 years from a country that didn't much care for lawyers, avoided their use, or found them only marginally useful and imported them from England...to a country insisting they have the absolutely most rigorously education, trained, and certified lawyers on the earth. According to the lawyers, anyway :) At this point there is hardly anyone alive today in the US that can remember a time when lawyers were not at the center of public life, or a requirement to conduct any business of significant scale.
Would requiring less education make the process cheaper, and allow more people to become lawyers in the US? Absolutely! Which is why it won't happen any time soon. More elected politicians are/were lawyers than any other profession, so getting them to vote in the debasement and dilution of their own profession is about as easy as getting them to vote themselves into being restricted by term limits. After all, how do you think so much legislation got written and passed that gave so much accreditation power to a private group like the ABA, or required a J.D. (while grandfathering in existing lawyers so they didn't have to go back to school)? I am quite certain there was no grass roots popular movement, with throngs of people taking to the streets to demand that lawyers spend more time in a University.
You could try to get a hierarchy established, where more cheaply educated (and lower paid) workers get less formal education while doing much of the work of the legal profession. Oops, never mind, we already have that: paralegal. If you review the requirements of what it takes to become a paralegal, you'll see it is remarkably similar to what was required of lawyers in the US prior to the 1960s. That is, 2-4 years of college (and it used to be even less), some additional specialized training, and you'd learn the rest on the job. This is but one example of the many ways that the relationship between a University education and the Professions have changed, and college degrees and graduate education have become required to join professions that used to require little more than a high school (secondary) education.
The times, they are a changin' (1964)