There is a very easy reason for the synoptic gospels. Mark wrote down a story using the Homeric tradition, and Matthew and Luke copied from Mark and some oral traditions (or the mysterious Q). Matthew and Luke did not copy from each other, which is why their nativity stories are mutually exclusive, as well as their geologies.
John is another beast all together. The GOJ was redacted on at least 4 times. It was called a gnostic work by one church father, and called an anti-gnostic work by another.
It isn't a 'grand conspiracy'.. it is just a developing tradition where one author copies another, then having the filtering process of
a central authority go through them, and change them for 'theological correctness'.