> if they were right, and complete, why would it seem good to luke to write another one?
No Gospel account is complete. I have a biography of Abraham Lincoln that's 600 pages, and it's different from other 600-pages bios of Lincoln. I have another one of General MacArthur of about the same length. Every historiographer is selective. Mark's Gospel is only 11,000 words, slightly longer than a max-length reddit post. There's no way it's complete. Matthew's is about 18,000 words (two reddit posts). There was more to be said. That's what I read between the lines.
> it's unclear whether or not he would be aware of matthew.
I agree. But's it hard to know what awareness or access to "Q" he might have had. We make so much out of "Q", but no reference to it or fragment of it (that we know of) has ever been found. It's quite the phantom theory in the mist.
> matthew the person, yes, may indeed be the source for Q. this is kind of a pet theory i have; the traditional attribution is that matthew wrote a sayings gospel in aramaic, which sounds an awful lot like a) the kind of thing an actual witness would write, and b) like and original language source for Q, which is greek. the gospel of matthew may have taken on that name because it contained the source that matthew actually wrote.
I have the same pet theory, and actually find myself in possible agreement with much of this. Suppose Matthew, living in Jerusalem, was actively telling and retelling the stories of Jesus. At one point he wrote down a bunch of it, especially the sayings (the 5 large blocks of speeches in Matthew), (possibly the logia to which Papias refers. As Mark and Matthew, along with others, circulated and spoke in Jerusalem and its environs, many of these stories took on set forms and were assembled into a document or series of documents ("Q"). Mark moved to Rome, spent some time with Peter, and used his exposure to Jesus (as a Jerusalemite and in a family of believers [Acts 12.12]), his exposure to Matthew, and his knowledge of Q to compose his Gospel. Matthew, reading Mark's Gospel a short time later, cribs blocks of it (since he was the source anyway) for his own Gospel, adding to it the logia that he had previously written down. Matthew's material is then possibly edited and enhanced by some later collaborators with other material from Mark, and we end up with Matthew's Gospel, "written" by Matthew, cribbed from Mark (of which Matthew may have been a source), including the logia, and possibly further redacted later by other contributors until it solidified into the Gospel we have today.
That could be why we have quotes from Matthew in the late 1st c., knowledge of the writing known to have Matthew as its tradent, and only later identified as "According to Matthew" by the late 2nd c.