The primary reason we have four gospels is that later Christians knew they were the oldest. The names were a later addition. Each has a different slant, which reflects not only the author but the author's community, as you point out. As Richard Burridge argued, the gospels are 1st century biographies in style, but not like the lives of great men of the time. Jesus was a nobody. And yet...

That said, they are tightly-written—until each gets to the resurrection. Then the tight narratives fall apart. None tried to describe the event, only its effect on the disciples. And even then the endings are clumsy, like Mark: "for they were afraid."

It is those internal discrepancies that are as important as the differing source materials.