Too often westerners, especially Americans speak of rights. The flip side to this is the reality of duty and responsibility. Both are needed.
The Holy Father speaks of the right of every person to hear the Gospel:
57. Like Christ during the time of His preaching, like the Twelve on the morning of Pentecost, the Church too sees before her an immense multitude of people who need the Gospel and have a right to it, for God “wants everyone to be saved and reach full knowledge of the truth.”[1 Tim 2:4]
He also speaks of the duty of the entire Church to preach it:
The Church is deeply aware of her duty to preach salvation to all. Knowing that the Gospel message is not reserved to a small group of the initiated, the privileged or the elect, but is destined for everyone, she shares Christ’s anguish at the sight of the wandering and exhausted crowds, “like sheep without a shepherd” and she often repeats His words: ”I feel sorry for all these people.”[Mt 9:36; 15:32] But the Church is also conscious of the fact that, if the preaching of the Gospel is to be effective, she must address her message to the heart of the multitudes, to communities of the faithful whose action can and must reach others.
Christianity is not a clique, or an enclave. The notion of a smaller, purer church goes against the very fabric of Christian duty. It might be that some of the people who receive preaching, baptism, and all are less than optimal in their words and actions. It doesn’t negate the Great Commission. Pope Paul VI doesn’t deny the need to care for the multitudes, those who are responsible for living the Christian life. Note the message is not for the mind, but for the heart. I would take that as less a kerygma aimed at emotions (affairs of the heart), and more a proclamation to the very core of human life (the innermost recesses).