Who wrote Matthew's Gospel and do we care?

Recently, I have been doing some reading on introductory issues to the Gospel of Matthew. One of the fascinating things about studying the synoptic Gospels (Matthew, Mark and Luke) is how much Matthew and Luke have in common with Mark's Gospel. Most scholars recognize what appears to be a high level of dependence on Mark as a source by the two other authors. In fact almost every verse in Mark is found in Matthew, Luke or both! Luke explicitly states that he did research before writing his Gospel and it makes sense that Matthew would have acted similarly.
Another interesting observation about Matthew's Gospel is that the Gospel has no claim to be written by the apostle Matthew (aka. Levi, formerly a tax collector). Our main reason for attributing it him as the author comes from several Church Fathers [Eusebius quoting a certain Papias (c. 125)]. This is strong external evidence (in other words evidence outside the Gospel itself). Even though there are difficulties understanding Papias' comments, they definitely indicate that Matthew wrote something.
A third interesting point about Matthew's Gospel comes from the previous two observations put together. If Matthew the apostle did write the Gospel and he used Mark as a source, then it is incredible that when he relates his own calling by Jesus (Matt 9) he uses Mark as his source! Perhaps by analogy this is the same as someone else writing your testimony of how you "got saved", and you using it instead of just writing your own version. This issue (and a few others) has caused Matthean authorship to be doubted by some biblical scholars.
But here is my point (finally, you may be saying); does it matter if Matthew wrote the Gospel or not? If there were an explicit, internal claim inside the Gospel itself that Matthew was the author, then I would say, "yes! it matters a lot", because then we have to evaluate whether the author was lying or being honest. But in this case no such self-acknowledgment exists. Perhaps we can treat Matthew's Gospel as we treat the book of Hebrews; included in the canon by the early church and therefore seen as authoritative presently, even though we don't know who wrote it.
Personally I think Matthew the apostle is the likely author based on the testimony of some of the early Church Fathers and some other arguments. I don't think I would die for this opinion though. Here is an area were conservative Christians who value "Matthew's" Gospel as authoritative and inspired need to be careful that we acknowledge the tentativeness of authorship for this book and not allow it to wreck our faith. Perhaps I am minimalizing something that means more for you. Are there other problems that develop from acknowledging only a tentative authorship for this Gospel?