Here's this little secret how the dentist association controls the number of dentists licensed each year - they raise and lower the difficulty of the licensing exams each year. Guess who wrote the exams? The existing dentists, who have incentive to restrict the number of new dentists. They can raise the difficulty with frivolous questions that don't impact the dental competency but weed out a number of qualified candidates.
I think the fact that a group controls its membership qualifications is not really a problem as long as other groups can compete with them to address the same needs. And without special treatment from the government. A level playing field, not subsidies for one model at the expense of other models.
Realtors control their numbers and qualifications too. But you can still be a real estate agent without being a Realtor. Having and protecting a brand is ok. Getting government to put some group in charge of all people addressing a need will raise prices.