Let me unpack that question.
First, you have to assume some level of accuracy is what is desired. There are more than a few schismatic and/or heretical factions (Byzantine and/or Slavic Protestant denominations, really) whose identity is wrapped up precisely in being *inaccurate*. That is, they do not want God's work to be known, either by science, or a clear view of current events, or the study of the ancient Fathers, or a united ecclesial witness, or much else. That is a blunt way to put it—and I have no intention of naming names here, just making the situation clear—but that's where it stands. So right away, you've got to be sure that general accuracy is what you want (and welcome to the forums, by the way—just be wary!).
Second, assuming you want accuracy, you have to define what you mean by accuracy. Accurate to the tropical year or the mean vernal equinox year? They are different. Accurate to the time of Jesus Christ or to now? They're also different—Earth's orbit changes, as does our planet's rotation. And then you've got the counterintuitive problem where you don't want the calendar to be *too* accurate. That is, it needs to be usable at the level of Eucharistic technology (at least farming, milling, fermentation, ovens, grafting, and a hundred other technologies that are perfectly feasible without computers), so the rules have to be relatively simple. Leap seconds are tough enough to do without computers, but think of how difficult it would be to coordinate leap milliseconds, if we accurately spaced the differing time throughout the year.
Third, none of this begins to touch on your qualifier of "useful". There are myriad concerns about consistency across the centuries. Granted, a lot of that can be overlooked—many saints are not commemorated on their day of death as it is, so the "lock-in" and historical importance of the current calendars is debatable. And on all the 3 most-used Christian calendars, spring is no longer March 25—it's shifted quite a bit. So the question of "useful" is perhaps even harder to answer than the question of accuracy, especially given the very loud denominations behind point #1 .
I was hoping to give you a short answer to your question, but, well, that *is* the short answer!