What does Luke 10:16 mean?
This is the summary statement of the first half of the chapter: it's about God, not us. Jesus is sending seventy-two disciples to preach the kingdom of God and call the people to repentance. They go to prepare cities He will visit. The disciples are to pray God will provide more messengers to reach those ready to listen. As they go, God will provide housing and food and make sure their personal needs are taken care of. If a town accepts their message, the disciples are to provide physical and spiritual restoration commensurate with God's kingdom, as empowered by Jesus, God the Son. If the cities don't accept them, God will judge them (Luke 10:1–15).The disciples are messengers, just as we are. If we spread the gospel of the Bible under the power and instruction of the Holy Spirit, those we speak to will react to God. If we rely on our own charisma and/or preach a gospel that does not align with what is in Scripture, our audience will follow or reject us. That's the goal of cult leaders, but it doesn't help anyone. We can't save. Only God can.
Many people today claim that they would follow Jesus if only they could see Him personally. His ministry on earth proves otherwise. Few people saw Jesus more than the people of Capernaum. Few witnessed more miracles of healing or saw more demons cast out. And yet, people still refused to accept Him as the Messiah. There is no reason to think the world would be different, today. We know it won't; Jesus will literally, physically reign from the throne in Jerusalem, and yet a great army from around the world will congregate and try to depose Him (Revelation 20:7–10). There is no proof great enough to convince everyone to follow Christ.