Vetting your own membership does not a monopoly make.
Every skilled profession requires peer-review admission to be legitimate.
I don’t see anything that suggests monopolies in any of the examples you have given.
I am not sure I can think of a who would be better for reviewing…say doctors.

The DOJ runins with the NAR were focused around 2 primary issues of contention.

1: It is unreasonable to require strict membership to actually read listings on the MLS.
(Pretty reasonable IMO)

2: It is unreasonable (and arguably price fixing) to require that membership in local Realtor boards and in the MLS be predicated on a specific fee schedule and service selection.
(This was because Help-U-Sell and other discounters were gaining market share and more established agents wanted to push them out of the market for RE services. Also, a very reasonable position by the DOJ).

In both cases, it was determined that the NAR was acting unfairly.

However, I am not aware of it ever being established (or even imputed outside blogs) that the NAR was a functioning Monopoly. The fact that competition exists means that if the NAR were a single business (Its not. Its a trade organization.) it would have an arguable hegemony but not a monopoly.