The prohibition is explicit rather than inferred. The Kitab-i-Aqdas abolishes the priesthood, forbids the pulpit as a raised place from which one person addresses the community with authority, abolishes auricular confession to another human being, and directs that asceticism and the monastic life be set aside in favour of work and family life within society. Alongside these the Baha writings make individual investigation of truth an obligation, so that a believer is not to accept a religious claim on the authority of another person.
The historical setting explains the force of it. The Bab and Baha'u'llah both taught in a Shia environment with a large, learned and powerful clerical establishment, and both faced its opposition directly. A revelation that removes the office removes the mechanism by which a religious class can stand between a person and the divine, and Baha writing presents this as the intended consequence rather than a side effect.
What replaces the office is a division of function. Elected bodies govern: Local and National Spiritual Assemblies, and the Universal House of Justice, first elected in 1963, which is the head of the Faith and which legislates on matters the scriptures leave open. Appointed individuals advise and encourage: Continental Counsellors and Auxiliary Board members, and formerly the Hands of the Cause of God, a rank now closed. Neither performs sacraments, hears confession, or interprets scripture on behalf of others.