What about the drift in the Gregorian calendar? Solar day and tropical year do not have a least common multiple.
Earth's rotation is — arguably — better measured against the stars, so a sidereal day is more "correct", yet it would not map to our daily routine at all.
So I believe the question is not what is more "correct" (we've long established that we are dealing with approximations at best, Julian calendar included: it already had leap years), but what is more useful? And that's what has driven adoption of the Gregorian calendar in most of the world, but I am fine if somewhere it's more useful not to have to worry about did some days just disappear at some point in the past.
I mean the answer is pretty simple: Neither is perfect, but the Gregorian calendar is objectively more correct. It has a small amount of drift, but the drift is less than the Julian calendar. This also makes it more useful, because it will be able to predict solstices and equinoxes (and other dates needed for scheduling planting and harvesting of crops) more accurately than the Julian calendar. Its overwhelming dominance is evidence that not many people care about the ~2 weeks that disappeared a couple hundred years ago.
You missed my point: where continuous dates are useful, it's ok not to care about two weeks of discrepancy even today. Basically, I am saying is that the biggest advantage of the Gregorian calendar today is its prevalance: all the other things matter less.
You also seem to be overstating the importance of exact dates when it comes to agriculture: my experience is that +-13 days does not make a practical difference, especially if it slowly accumulates (it's not like you would suddenly have to do the harvest 13 days later from one year to the next — you actuslly had to do it 10-13 days "early" once the calendar was switched, and it didn't make a difference even then).
If human civilization continued using the Julian calendar, we wouldn't have been any worse off: nothing points at it that we would have been. I am not saying that Gregorian calendar is "worse" at all (though those born on Feb 29 might beg to disagree when they go 8 years between birthdays 2096-2104 :)), just that where it's better does not matter much.
Earth's rotation is — arguably — better measured against the stars, so a sidereal day is more "correct", yet it would not map to our daily routine at all.
So I believe the question is not what is more "correct" (we've long established that we are dealing with approximations at best, Julian calendar included: it already had leap years), but what is more useful? And that's what has driven adoption of the Gregorian calendar in most of the world, but I am fine if somewhere it's more useful not to have to worry about did some days just disappear at some point in the past.