In our Enterprise-era RPG (which is rapidly approaching the "early Federation"-era) we decided to make a fictional "Federation year", which was averaged out from the lengths of years of the four founding members, with a Kelvin-style stardate system based on that calendar.Why do that when you can use an arbitrary, culturally-neutral numerical system that applies universally?

Unless this is referring to writing novelizations, no. With all due respect to cover bands, tie-in writers do a lot more than just playing the same tunes with a bit of a twist. If anything, we're the support act...