Concerning your observation that "a number of paid ministers consider continuing education to be optional,” I believe it is important to remember that Jesus was never “educated" (John 7:15), and his disciples were "unschooled" (Acts 4:13). Not to say I disagree that we all need a deeper knowledge of the Bible…
I appreciate your concern. It is possible to put too much stock in academia. Yet we must take account of the fact that Jesus trained his apostles for three years. He trained them in how to live, but also in how to understand and present God's Word.
Peter’s Pentecost message is brilliant—notice the way he handles the scriptures, his mastery of the Old Testament. Of course Peter and John weren’t the equivalent of modern PhDs, theologians in ivory towers, publishing dense tomes intelligible only to fellow scholars.
The salient point in Acts 4:13 isn’t that Peter and John hadn’t studied, but that they had been with Jesus. He was their teacher. They were indeed biblically trained—just not in the establishment schools. (Which made the establishment uneasy.) Their having been with Jesus explained not only of their command of Scripture, but also the power of their faith.