Wow.
Lots of problems with the facts here.
The California Bar is not a private organization.
It is an administrative arm of the California Supreme Court.
It is, by definition, part of the government.
The term monopoly does not generally apply to governments.
The CAR (AKA CREA) does not hold public regulatory standing in the same way and is therefore not analogous.
Peer review applies to all the occupations you mentioned.
The level of government involvement varies in that some review bodies are government employees (one step removed) and others are accredited by government (2 steps removed) and still other review bodies who are accredited by private accreditation firms who are commissioned by government (3 steps removed). Most educational advancement falls into the third category. You get your PhD application reviewed by PhD’s whose instruction is accredited by a private company who is licensed by the Department of Education.
Teaching credentials are not much different.
And honestly, if the barriers seem are too high, then the applicant should be looking for another line of work.
The loads of excess (read jobless) credentialed teachers (often NEA members) speak to the relative lowness of those barriers.
Your assertion that the NAR functions as a monopoly also flies in the face of like half the industry.
Most licensed agents are not members. There is no requirement to be a member to sell property, negotiate property contracts, rent property, use CAR forms, or join the MLS.
Also, those statutes are applicable any time that there are allegations of unfair asymmetrical competition.
The NAR’s conduct was certainly unfair but it meets none of the minimum criteria for monopoly.