All of my books with "Synoptic problem" in the title are either primarily or entirely focused on the question of dependencies. It is a "problem" rather than merely a "question" because there is no completely satisfactory answer to this issue. I am not sure those who see inconsistencies see the purported inconsistencies as being particularly problematic.
Questions about who wrote first will still have an historical interest (though I have yet to see any information that the relative dating of Matthew, Mark, and Luke would make a plugged ha'p'orth of difference to interpretation), but if you assume that things happened as described that does provide a common source for a great part of the material; and it eliminates certain issues, like the attempt to make John's temple cleansing the same as that of the synoptic writers.
Again I agree to a certain extent. When one has various accounts of similar events, one has to decide whether the differences in the accounts can best be explained by it being different events being described, or by different viewpoints on the same event. There isn't one approach to these issues which is
guaranteed to produce the right ("sound") answer.
Steve, thank you or your kind reply. Since this is your field of expertise, I have no doubt you have read far more widely than I. In my limited reading about these matters, the synoptic problem and the quest for the historical Jesus are linked, and the fact of literary relationship and variation among the synoptic gospels is put forward as evidence for the hypothesis that parts of the Gospels have to be discounted as being historically valid. I am away from home at the moment, so can only refer to John C. Dwyer, The Word Was Made Flesh, pp.61,62:
The texts given here and the observations we make about them obviously do not prove that Mark was the first to write a Gospel and that Matthew and Luke copied from him. They offer a very small sampling of the kinds of evidence which nineteenth century scholars sifted and weighed, and which led them to virtual certainty about the priority of Mark. This was an extremely important conclusion for two reasons. First, even in the earliest times, no one had ever claimed that Mark was an eye-witness of the events which he recounts, and it seems clear that if Matthew had been an eyewitness, he would not have used Mark’s Gospel as a source. In other words, the priority of Mark really invalidated the claim that Matthew was an eyewitness. Second, as a consequence of this «displacing» of Matthew, Mark was now seen to be to be the Gospel which brings us closest to the events of Jesus’ life. There was another very important consequence of the priority of Mark. In places where Matthew and Luke seem quite close to Mark, wecan often notice small differences - certain words left out, for example, or certain subtle changes in the events recounted, all of which seem to point in a single direction. For example, in the story of the cure of the man with leprosy (Mark 1:40-45; Mt 8:1-4; Luke 5:12-16), we find that Mark notes Jesus’ reaction when the leper comes and asks to be healed: Jesus is «deeply moved» («shaken» would be a possible translation). And when the cure itself is described, Mark notes that Jesus was «visibly and audibly angry.» (The emotional reaction may be the residue of a more primitive version which told of Jesus’ reaction to the demonic power which was responsible for the disease.) Most of these referencesare absent in Matthew and Luke, and it is hard to avoid the impression that the strong emotion which is reflected in verse 41 of Mark’s version of the story was felt, by the time Matthew and Luke wrote, to be inappropriate for Jesus. This type of editing appears just frequently enough to justify our speaking of a certain sense of embarrassment on the part of Matthew and Luke at a very human Jesus, who could be gripped by deep emotion. The process of making Jesus conform to human ideas of what «God in human form» should look like, had begun within the New Testament and did not wait for a later theology. Awareness of this would eventually bring scholars to raise the question of how Mark himself might have modified the oral tradition which he found; but in the nineteenth century it merely confirmed their suspicions about the priority of Mark and it led scholars to rely on Mark’s Gospel as they sought to draw the picture of the Jesus of history.
Certainly, it is always a valid question whether an event is described differently because it was a different event or because the narrator has a different standpoint and purpose; but claiming a contradiction in the dating of Christ cleansing the Temple, or in the setting and content of the Sermon on the Mount, becomes pointless if one accepts that the Gospel writers wrote accurately, so that if time and setting are described in terms that are incompatible, the reference must be to different events.