Aside from often given students more of a "feel" for history than (often quite dull) textbook reading, primary sources are used to teach how to critically engage with the past, and how historians do their craft. Rather than undermine the historian's position, it strengthens it: it shows that these are not matters of faith, but matters of interpretation, and models the kind of careful analysis that must be brought to all sources, historical and present-day.
We do attempt to do these other things, how to synthesize various interpretations and viewpoints, as well. But the goal of a history class is not merely to make one learn to trust experts (which experts, anyway?), any more than a science class is. The goal is to promote critical thinking and engagement with the subject. Education that is based on recitation and dogma tends not to "stick," and is easily replaced by someone else's dogma.
Give a student a historical narrative, and they're set for a day. Teach a student to think critically about the past and they're set for life. If you think that only historians needs to think critically about the past, and about history, I assure you, no historians think this. History is alive and motivates our lives, our politics, our decisions. Memorizing a few facts doesn't cut it. I think you underestimate the value of a sense of history, and underestimate the students.