One needn't believe that the Father and the Son continue to speak face-to-face with each succeeding prophet. Perhaps they do speak, but it isn't necessary to the faith that they do. It would be enough that God continues to inspire and lead them in whatever way he chooses.
One needn't believe that the prophets are infallible. I assume that they are righteous people, but I also assume that there are more-or-less ordinary people in my congregation who are their equal in righteousness. Prophets are not called because they are more righteous than everyone else, but because, being sufficiently righteous, they have the skills, attitudes, and abilities that God needs for a particular time and work.
Mormon explanations for why we believe in continuing revelation are likely to vary. But Mormon belief that the Church is led by continuing revelation is central to the identity of the LDS Church and its members.