[zajio1am]

I would say that the purpose of the calendar is tracking time/days in general. Astronomical events are just used as a tool to do that. Earlier calendars were lunar-based instead of solar-based, as keeping synchronized with moon is easier.

[dangerbird2]

The solar cycle is extremely important for premodern agricultural societies, since it allows predicting growing and harvesting seasons. If you're going by the Julian calendar and the Autumn equinox is falling on September 10, there's probably going to be confusion as to when the harvest should occur. In the case of the Gregorian Calendar, Catholic countries rely on the Spring Equinox to schedule Easter, and when it started occurring well before March 21, this made it increasingly difficult to synchronize the religious and secular calendars.

[necovek]

While it's somewhat true, most of the people in premodern agricultural societies couldn't read (especially those concerned with when the harvest should happen), and probably couldn't care less about dates in the calendar. Even today, weather and actual crop lifecycle plays a larger role in agriculture than particular dates.

Even if people were tracking dates, adjusting for a couple of days every 200 years wouldn't be that hard: nobody would remember the good old times when we did the harvest on September 22nd in 1234, and now we do them on September 20th in 1434.

Finally, matching up with astronomical events would sometimes put sidereal year (and day) at the forefront: a day that's ~4 minutes shorter than the solar day making the tropical year Gregorian calendar is based on. Things get murky quite quickly once you start going down that path of what "correct" really is.

Note that in the Gregorian calendar, Spring equinox in 2021 and 2022 fell or falls on March 20th. It's only pretty good when averaged out over a 400-year cycle.

Basically, all of these calendar systems are attempts to "square the circle": find something resembling the least common multiple of non-integer values (solar day length and tropical year length), and then try to mix in a bunch of events observed in a different coordinate system (to overly simplify it, all the night stuff is "sidereal").

So we get back to what is really "useful"?

If you don't care about knowing how many days ago, or on what date in the proleptic calendar of your choice something happened in the past just from the date inscribed on it (eg. imagine a letter dated January 5th, 1605), you would certainly be fine with just dropping 10-13 days somewhere along the way. I can, however, understand when someone thinks it's easier to be off from astronomical events for a few weeks to avoid all that administrative trouble, for instance. However, the biggest practical problem today would be that everyone else has written those 10-13 days off, so it's probably easiest to switch too, especially in the global world we've got today.

But there is nothing intrinsically better in the Gregorian calendar that makes it win on all counts. It's just another agreed-upon approximation.