That’s not how laws work. Just because you personally see a way it can be philosophically generalized or conceptually generalized does not mean laws apply the same to all generalizations. Brokers, exchanges, investment firms, banks, etc., all have specific legal obligations based on different types of fiduciary duty, different service offerings, etc. It can easily be the case that an exchange entity has a legal ability to deny access through delisting while a broker entity does not have the right to deny service in some particular scenario.
I am not saying what the case is for brokers today, but regardless, appealing to some notion of proof by contradiction because of generalizing a behavior is not a valid way to analyze the situation.