The four Gospels that were centuries later put under one cover. They lasted for 300 years as separate sources.
While you are correct that the gospels are four independent records of Jesus, they did begin to travel together earlier than you said.
P45 is dated around 250, so even if you go with an early date for the writing of the gospels, that’s still under 200 years before they were bound together that we know of, they could have traveled all together even before this codex was created.
This is important because people like to claim that it was much later that someone “decided” which gospels to keep and which to exclude. In reality Christians knew early on which gospels were legitimate and which ones such as the gnostic gospels were illegitimate forgeries.
https://www.historyofinformation.com/detail.php?entryid=3539